text:
vin number scanner android app Workers and Jobs | Freelancer
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an apps for presence...main requirements which solution should be in Android Platform.
Game to Pick Which Number is Bigger. Both Android and IPhone.
Need an App that shows two pictures of numbers and the user have to select which is bigger then shows...within 2 days for each platform. Please add up the number of letters in the word pinterest and put that in
You must have done a...implementation, testing/results, conclusion. Maximum number of pages maybe 60. We have done the first 3 chapters...of work before and have coding knowledge with android.
Miracasting on Android App
...expert to help me in developing Miracast App, the role of this app will be to mirror whats-so-ever is playing...windows or Ubuntu as required] to All connected android devices. these tablet are connected to PC / Server...Server on intranet or local network. Total number of devices will be 20-25. So Whatever in open on PC
Android, CMS, Video Broadcasting
...want to offer them a mobile app. that can be used only by limited number of people (the invitees only)
Mar 17, 2015Ends - 2h 21m
The user can choose...disabled.
1) Login with LinkedIn, Facebook...external links
9) Mapping of users 10) Records number of select type of videos completed on user profile...Videos/Audios that the user completes in a given number of months increasing star rating of the user. this
I am looking for someone to build me an Android application that will automatically and immediately print...printed.
This application will be installed on Android phones and use bluetooth to communicate with the...code. The user also needs to be able to set the number of copies of each order to be printed.
The app captures the following information: Name, Passport/ID number, phone number, ID number of those...those they want to send money to, phone number of those they want to send money to, Name of those they...customer's ID or passport (which is compressed by the app) and lastly the signature from the customer.
Android App. ...of a simple 2 screen iOS app and I am now looking at porting it to Android. As a result, this is not...is enough and I can edit the rest. Skills the app requires:
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Android app We need in WordPress based android app maker to help us getting data structure of WordPress multi site
Android, Wordpress, CSS
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- Login with Facebook (twitter...Status (should be sent to see TRACKING POSTAL MAIL NUMBER)
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Android App Project Report Writing/Dissertation
You must have done a...implementation, testing/results, conclusion. Maximum number of pages maybe 60 in total for all chapters. We...of work before and have coding knowledge with android.
...someone to create an Android Personal Finance Budget app for my business. The app should be functional...functional and professional. The app should also follow the branding of my business.
Write an Android application I have a number of app ideas that I believe will take mobile apps and games to new heights -generating...-generating respectable profits. The success of these app ideas will depend largely on the quality of their development...apps. I require
You will be forming a rather unique
Gambling Software Website and App
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We would like...Gambling Software based on buy tickets with a random number on it and every week at Friday the Software should...World card and a random Number generator and choose depending on the number of Players up to 100 different
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I dont need any special app coz it will be used just for my childs (personal
Write an Android & IOS app i need a similar app like OLA i=
Mar 27, 2015Ends - 22h 16m
...specific range and chat. The app will not require users to login, instead phone number shall be used as a login...login (as in Viber).
Mar 9, 2015Ends - 5d 15h
We are looking for new app testers to test out the latest apps........we are looking for people...people who have an IOS or ANDROID device....... The person who can make the best review in 200 words
Design for Android App - Health Design of screens for an AndroidiOS app, including:
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3....creating an app
Preference for freelancers who can also implement the app in AndroidiOS
Mar 26, 2015Ends - 7d 23h
...the radio list and scroll down on this list, the app gets off
Bug 4 : the service does not work. If you...the notification bar you don’t kill completely the app
Bug 5 : the social networks. 2 resources must be
Port Android App to IOS Details about the Android App are as follows: 1. Currently developed using Parse Mobile Application...Tags which will be disabled on iOS Devices 5. The App requires the use of Mobile Push Notifications
I am in need of a simple Android app to be developed for me. This app will need to have a way for me...daily. The purpose of this app is for daily sports picks.
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bid if you have both Android and web developer
Android, HTML, MySQL, PHP, Website Design
...and now we need to develop the mobile apps. The app suppose to let users do following:
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I need a developer for an android Sudoku app. 1.	Puzzles will be supplied by me. 2...User can play as a guest or login/register. 3.	App communicates with server via API's. So you need to...selected bidders will receive full documentation.
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We want to get the front end of our android application. We have the completed design and backend... 2) For the first time users we have a phone number verification system
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Android, Mobile App Testing, Mobile Phone
Mar 29, 2015Ends - 4d $360

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text:
The Renaissance portrait : from Donatello to Bellini (Book, 2011) [WorldCat.org]
Title: The Renaissance portrait : from Donatello to Bellini
Author: Keith Christiansen; Stefan Weppelmann; Patricia Lee Rubin; Bode-Museum; Metropolitan Museum of Art (New York, N.Y.)
Publisher: New York : New Haven [Conn.] : Metropolitan Museum of Art ; Distributed by Yale University Press, 2011.
In the words of the historian Jacob Burkhardt, 15th-century Italy was 'the place where the notion of the individual was born'. In keeping with this notion, early Renaissance Italy also hosted the first great age of portraiture in Europe. This title provides research and insight into the early history of portraiture.
Publisher Synopsis Selected as a "Choice" Outstanding Academic 2012 Title for Fine Arts within the Humanities category.--Outstanding Academic Title"Choice" (05/22/2013)
Add tags for "The Renaissance portrait : from Donatello to Bellini".
November 2011 New Books(16 items)
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type: global

value: This website is a union catalog that itemizes the collections of 15,637 libraries in 107 countries that participate in the OCLC global cooperative. It is operated by OCLC, Inc.


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Genuine Garnet Rings | Groupon Goods
QR6919G-SSR
Total carat weight: 1.56 CTTW
Shape: marquise center with trillion accent stones
Full dimensions: 10.92mm x 13.46mm x 4.83mm
QR16385GWT-SSR
Stone type: garnet and white topaz
Total number of stones: 3 garnet pieces and 6 white topaz pieces
Total carat weight: 1.97 CTTW
Full dimensions: 7.87mm x 18.54mm x 5.59mm
QR16714GWT-SSR
Total number of stones: 3 garnet pieces and 16 white topaz
Full dimensions: 10.41mm x 18.29mm x 5.08mm

value: This website is an American global e-commerce marketplace connecting subscribers with local merchants by offering activities, travel, goods and services in 15 countries. Based in Chicago, Groupon was launched there in November 2008, launching soon after in Boston, New York City and Toronto.


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THE 10 CLOSEST Hotels to Synagoga Mikulov - TripAdvisor - Find Hotels Near Synagoga Mikulov
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value: This website is an American online travel company that operates a website and mobile app with user-generated content and a comparison shopping website.


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Places To Eat in Woodstock, Georgia with Reviews & Ratings - YP.comFind People•Advertise With UsBrowseFind PeopleFeatured CollectionsRestaurantsAutomotiveHome ImprovementHealth & WellnessAttorneysPeople Searched For...AttorneysDentistsTree ServiceElectriciansPediatric DentistryPlumbersVeterinariansFamily Law AttorneysGarbage CollectionAuto Repair & ServiceUsed Car DealersMoversTowingAutomobile Salvage24 Hour Urgent CareTaxisRoofing ContractorsUsed & Rebuilt Auto PartsAnimal Removal ServicesPainting ContractorsMajor Appliance PartsTax Return PreparationTemporary Employment AgenciesAre you alocal business owner?Advertise with YPor call 888-367-2194What do you want to find?Search by business name, or keywordnearWhere? 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Make a Reservation.2335 Mansell Road, Alpharetta, GA 30022www.bucadibeppo.comOnline OrderingJoin our eClubFind Your LocationCateringReservationsAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection1. LongHorn SteakhouseMenu(2)1420 Towne Lake PkwyWoodstock, GA 30189(770) 924-5494RestaurantsAmerican RestaurantsWebsiteDirectionsMore InfoThe best Parmesan crust filet steak! Service was great! Had Parmesan crusted asparagus a few weeks ago and loved it too! Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection2. Tuscany Italian RestaurantMenu(7)250 Cinema VwWoodstock, GA 30189(678) 453-0888Italian RestaurantsWebsiteYou might not expect authentic Italian fare and an excellent, albeit somewhat small, setting to showcase it in to be in a Publix stripmall. But tha…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection3. The Magnolia Thomas RestaurantMenu(4)108 Arnold Mill RdWoodstock, GA 30188(678) 445-5789Breakfast, Brunch & Lunch RestaurantsWebsiteBook a Table »Dining at The Magnolia Thomas House was one of the best dining experiences I've ever had. I would give the food, the ambiance, and the incredible st…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection4. Freight Kitchen & TapMenu(1)251 E Main StWoodstock, GA 30188(770) 924-0144American RestaurantsRestaurantsWebsiteTook my wife out to dinner here the other day. Excellent burger and fries delicious and the waiter recommended an excellent beer to go with it. My w…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection5. La Parrilla Mexican RestaurantMenu(10)1065 Buckhead XingWoodstock, GA 30189(770) 928-3606Mexican RestaurantsBarsWebsiteOrder OnlineTook mom and daughter sunday night and they had live music that was great and the food is so fresh and prepared beautifully. I had the chicken mila…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection6. Song's GardenMenu(2)4451 Towne Lake PkwyWoodstock, GA 30189(770) 928-8387Chinese RestaurantsAsian RestaurantsWebsiteBeen ordering from them for 8 years and the food and service is always amazing....Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection7. Panera BreadMenuView all 13 Locations2625 Towne Lake PkwyWoodstock, GA 30189(678) 813-4809Sandwich ShopsAmerican RestaurantsWebsiteFrom Business: From focusing on quality, clean ingredients to serving our food to you in a warm and welcoming environment, Panera Bread is committed to being an ally to our guests…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection8. Jump Kitchen Saloon1085 Buckhead Xing Suite 140Woodstock, GA 30189(678) 388-7717RestaurantsSports BarsWebsiteAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection9. Donovan's Irish Cobbler1025 Rose Creek Dr Ste 500Woodstock, GA 30189(770) 693-8763Irish RestaurantsBarsWebsiteAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection10. Gustons GrilleMenu(1)12195 Highway 92Woodstock, GA 30188(770) 485-6565Barbecue RestaurantsBarsBar & GrillsI've been working for this company for the last 5 years! I wouldn't even consider leaving. Guston's goes above and beyond what any regular restaura…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection11. Taste Of ItalyMenu(1)8265 Highway 92 Ste 106Woodstock, GA 30189(770) 928-3764Italian RestaurantsCaterersWebsiteOrder OnlineIf you are from the northeast, where there is great pizza, you will love their food and pizza. By far, the best I've found in my 12 years in Georgi…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection12. Papa P'sMenu(3)2295 Towne Lake PkwyWoodstock, GA 30189(770) 592-3100Mexican RestaurantsBarsCaterersWebsitedelicious guacamole. Fresh and tasty. I will order it every time I come in. Goes well with their chicken soupAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection13. Hacienda Vieja290 Molly LnWoodstock, GA 30189(770) 517-7958Mexican RestaurantsWebsiteAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection14. Corner BistroMenu(3)2360 Towne Lake Pkwy Ste 110Woodstock, GA 30189(770) 924-1202American RestaurantsRestaurantsWebsiteOrder OnlineIf you like friendly service, large portions, great prices and all homemade then you need to try this place. They have awesome sandwiches and sal…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection15. Fire Stone Wood Fire Pizza & GrillMenu(4)120 Chambers StWoodstock, GA 30188(770) 926-6778PizzaItalian RestaurantsRestaurantsWebsiteBook a Table »Tried the pizza on Dec. 16, 2014 and it is without a doubt one of if not the best pizzas I have ever had. The dough,the sauce, and the toppings were…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection16. Yen Ching Chinese RestaurantMenu9105 Hickory Flat HwyWoodstock, GA 30188(770) 346-0899Chinese RestaurantsTake Out RestaurantsWebsiteOrder OnlineAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection17. Tacos & Beer Mexican RestaurantMenu(2)5335 Old Highway 5Woodstock, GA 30188(678) 445-0762Mexican RestaurantsBarsWebsiteAmazing food, great staff, superb drinks! A fabulous local gem. Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection18. O'Charley’s Restaurant & BarMenu(1)View all 5 Locations10009 Highway 92Woodstock, GA 30188(770) 592-7501American RestaurantsRestaurantsWebsiteOrder OnlineThe food at this location is good and so is the service. O'Charleys has good food that is a bit pricey.Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection19. Hot Dog HeavenMenu(10)8558 Main StWoodstock, GA 30188(770) 591-5605Hamburgers & Hot Dogsprompt service and the always friendly Becky serves you up a fresh hot dog on the spot. She even remembers your name upon entry.........that's ama…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection20. Family Tradition RestaurantMenu7830 Hickory Flat HwyWoodstock, GA 30188(770) 345-7117American RestaurantsWebsiteFrom Business: Family Tradition Restaurant & Catering offers a range of food items and beverages for breakfast, lunch and dinner. The restaurant specializes in southern-style meat…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection21. Kani House Japanese Japanese Steakhouse & SushiMenu(8)2455 Towne Lake Pkwy Ste 110Woodstock, GA 30189(770) 592-5264Japanese RestaurantsAsian RestaurantsWebsiteOrder OnlineWhat a great experience! My Mama and I went there for her birthday and had a great time. Our Hibachi Chef, DD was super fun and did a great job on t…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection22. CiCi's PizzaMenu(2)View all 4 Locations12186 Highway 92 Ste 110Woodstock, GA 30188(770) 592-6885PizzaRestaurantsTake Out RestaurantsWebsiteI think their pizza is just ok but it's really family friendly and the kids like it a lot. You can get in, get your pizza without waiting. Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection23. Restoration Cuisine108 Arnold Mill RdWoodstock, GA 30188(678) 445-5789RestaurantsAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection24. Props N Hops1001 Victoria Landing DrWoodstock, GA 30189(678) 919-7802American RestaurantsRestaurantsAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection25. 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Tea Leaves & Thyme8990 Main StWoodstock, GA 30188(770) 516-2609Take Out RestaurantsRestaurantsWebsiteAdd to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection28. Izzy's Kouzina(8)5947 Holly Springs PkwyWoodstock, GA 30188(678) 403-1184RestaurantsWebsiteWe are from Detroit and have been looking for a good pizza since we have moved down south. We may have found it at Izzy's! I look forward to try…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection29. Reel Seafood(6)8670 Main StWoodstock, GA 30188(770) 627-3006Seafood RestaurantsWebsiteIf you're OTP in Woodstock, this is as good as it gets for seafood. Executive chef & proprietor David Silverman cut his chops in Atlanta's fine di…Add to mybookRemove from mybookAdded to your food collection!Error when adding to food collectionThis business was removed from the food collection30. Chili's Grill & BarMenu(4)View all 9 Locations1460 Towne Lake PkwyWoodstock, GA 30189(770) 592-7676American RestaurantsRestaurantsBarsWebsitethis is not the right number.Related Articlesfor Places To Eatmore related articles »Game Day Must-Dos »Some sports fans like to rock up to a bar and cheer on their team. Others live for the traditions: tailgating, party-hosting, and dressing head-to-toe in fan apparel. Here are so…The July To-Do List »Use YP's sizzling summer checklist to pack in as many backyard barbecues, family trips, and memorable outings as you can before the kids head back to school.Family-Style RestaurantEnjoy Family-Style Italian at Buca.Any Size Group. 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of 2325results12345NextAdd a New CollectionOops! There was a problem saving the new custom collection.Please try again.Collection Name cannot be emptyUpload a Photo(optional)Remaining Characters: 100Remaining Characters: 500CancelSaveMap ViewFeatured Restaurantsin Woodstock, GeorgiaRed Lobster(1)Find a LocationWebsiteMore InfoThe Border Mexican Restaurant(84)2569 Cobb Pkwy SE, Smyrna, GA 30080(770) 818-0650Best mexican food north of the borderWebsiteVirtual TourDirectionsMore InfoMarietta Pizza Company(13)3 Whitlock Ave SW, Marietta, GA 30064(678) 265-1280WebsiteDirectionsMore InfoMarietta Pizza Company(4)3901 Mary Eliza Trce NW, Marietta, GA 30064(678) 269-4465WebsiteDirectionsMore InfoJR's Log House Restaurant(10)6601 Peachtree Industrial Blvd, Norcross, GA 30092(470) 299-9007WebsiteDirectionsMore InfoAgatha's A Taste Of Mystery(26)161 Peachtree Center Ave NE, Atlanta, GA 30303(404) 584-2255WebsiteDirectionsMore InfoChantico Burrito Cantina25 Powder Springs St, Marietta, GA 30064(678) 265-6224WebsiteDirectionsMore InfoOlive Garden Italian Restaurant(3)2467 Cobb Pkwy SE, Smyrna, GA 30080Other Locations »(888) 976-9578Buy One, Take One is back! Click to learn more.WebsiteDirectionsMore InfoLongHorn Steakhouse(2)1420 Towne Lake Pkwy, Woodstock, GA 30189Other Locations »(770) 924-5494WebsiteDirectionsMore InfoProvino's Italian Restaurant(1)3420 Buford Dr, Buford, GA 30519(770) 904-0242WebsiteFind a LocationDirectionsMore InfoSonny's Real Pit Bar-B-QServing the Woodstock area.(770) 368-1653Contact Us for InformationWebsiteMore InfoOlive Garden Italian Restaurant429 Ernest W Barrett Pkwy NW, Kennesaw, GA 30144(888) 857-7452Buy One, Take One is back! Click to learn more.WebsiteDirectionsMore InfoLongHorn Steakhouse(6)2700 Town Center Dr NW, Kennesaw, GA 30144(770) 421-1101WebsiteDirectionsMore InfoLongHorn Steakhouse(2)3366 Cobb Pkwy NW, Acworth, GA 30101(770) 975-8703WebsiteDirectionsMore InfoLongHorn Steakhouse4721 Lower Roswell Rd, Marietta, GA 30068(770) 977-3045WebsiteDirectionsMore InfoLongHorn Steakhouse2636 Dallas Hwy SW, Marietta, GA 30064(770) 514-0245WebsiteDirectionsMore InfoDidn't find what you were looking for?magnifying glassPlease help others by helping us do better.Suggest a BusinessHelpful Reviews Mustards Last Standdc1ccc ratedLocally owned with awesome foodI have been a regular since they opened about a month ago and have always gotten quality food. Lots of variety on the menu. The wings and deli sandwiches are especially good. They also serve breakfast all day. As many times as I have eaten there I have NEVER seen anything that would give me cause for concern about eating there and have always been satisfied with me food and service. Maybe the first person to review was having a bad day. I HIGHLY recommend Mustard's and will continue to eat there.Izzy's KouzinaKat R. ratedAuthentic Greek restaurant run by a real Greek family! We've already been several times since they opened and have tried many things on the menu. Greek salad, souvlaki, fried ravioli, fried mozzarella are all delicious! On our last visit, we had the lasagna and the chicken parmesan. We've heard their pizzas are awesome too so we plan to try those next! You must order the cheesecake for dessert! Slices are huge & delicious!Izzy's KouzinaCarolina M. ratedIzzy's Kouzina is a very nice and refreshing addition to the area. Me and my family love this restaurant. The food tastes very fresh and the serving sizes are large. I personally love the salads, the spanakopita ( so good and fresh), the toasted ravioli, and the cheese fries. The ice cream is delicious! I can't wait to visit them again to try more Greek and Italian food!AboutAbout UsSite FeedbackContact UsAdvertise with UsCareers - We're HiringCorporate BlogEngineering BlogLegal

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MY Hostel Nampo بوسان حجز رخيص فوري مع اجودا دعم عملاء
?MY Hostel Nampo هل لديك سؤال بخصوص
Wi-fi system is bad. I received a very weak signal in my room. No wifi for upper floors. تاريخ التقييم 04 يوليه 2016
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It would be great if the door's passcode was told to us before arriving. Otherwise, all was very good. تاريخ التقييم 02 ديسمبر 2016
جونج جو بوسان, كوريا الجنوبية

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User talk:Carlasherman Genealogy - FamilySearch Wiki
User talk:Carlasherman
Hello, Carlasherman, and welcome to FamilySearch Wiki! Thank you for your contributions. We hope you like this place and decide to stay. Here are some pages that you might find helpful:
Introduction The Guiding Principles of FamilySearch Wiki Get started with this site Search for Articles Help:Edit and Contribute Manual of Style Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your username and the date. If you need help, ask me on my talk page, or place {{helpme}} on your talk page and ask your question there. Again, welcome! Steve 09:48, 31 October 2009 (UTC)
Thank you for your contributions. We need your feedback! Our goal is for wiki.familysearch.org to be a friendly, welcoming place that is easy for you to use and make contributions. Please share your comments. What is your experience? What challenges do you face in using and contributing to the wiki? Where do you find help? When you notice problems, please go to Challenges Facing New Users. This is the page for making comments on challenges you have encountered. Please post your comments and ideas for the solutions at What New Users and Contributors Want to Make Wiki Easier. Then, come add your "Vote" by listing and prioritizing those solutions that are most urgent and important for the entire community at Newbies Priorities. This is not only for newbies, we also need experienced user/contributor feedback on your early, new user experiences. Thank you! Kara aka CK Whipple 16:55, 7 November 2009 (UTC)
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Patent US7356100 - Estimating channel impulse response and equalizer coefficients in UWB ... - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inAdvanced Patent SearchPatentsA method estimates a channel impulse response in an ultra wide bandwidth (UWB) system. Multiple training sequences modulated at a chip rate are received. Each training sequence is sampled by parallel with multiple correlators at sampling rate substantially slower than the chip rate to obtain a samples...http://www.google.com/patents/US7356100?utm_source=gb-gplus-sharePatent US7356100 - Estimating channel impulse response and equalizer coefficients in UWB communication systemsAdvanced Patent SearchPublication numberUS7356100 B2Publication typeGrantApplication numberUS 10/616,875Publication dateApr 8, 2008Filing dateJul 10, 2003Priority dateMar 3, 2003Fee statusPaidAlso published asUS20040185787Publication number10616875, 616875, US 7356100 B2, US 7356100B2, US-B2-7356100, US7356100 B2, US7356100B2InventorsAndreas Molisch, Ye Li, Jinyun ZhangOriginal AssigneeMitsubishi Electric Research Laboratories, Inc.Export CitationBiBTeX, EndNote, RefManPatent Citations (17), Non-Patent Citations (2), Referenced by (7), Classifications (26), Legal Events (2) External Links: USPTO, USPTO Assignment, EspacenetEstimating channel impulse response and equalizer coefficients in UWB communication systemsUS 7356100 B2Abstract A method estimates a channel impulse response in an ultra wide bandwidth (UWB) system. Multiple training sequences modulated at a chip rate are received. Each training sequence is sampled by parallel with multiple correlators at sampling rate substantially slower than the chip rate to obtain a samples over a time interval of the impulse response at a resolution substantially equal to the chip rate, and then estimating the channel impulse response from these samples.
1. A method for estimating a channel impulse response in an ultra wide bandwidth (UWB) system comprising the steps of:
generating a training sequence;
modulating the training sequence at a chip rate to produce a modulated training sequence, the modulated training sequence being comprised of ultra wide bandwith radio pulses;
generating a training signal comprised of a plurality of repetitions of the modulated training sequence;
transmitting and receiving, via a channel, the training signal;
sampling the received training signal, in parallel, with a set of correlators to obtain a plurality of samples, in which each correlator samples the received training signal at a sampling rate substantially slower than the chip rate, each correlator samples the received training signal at a different delay for each repetition of the modulated training sequence in the received training signal, and such that the plurality of samples spans a time interval corresponding to an impulse response of the channel at a resolution substantially equal to the chip rate; and
estimating the impulse response of the channel over the time interval corresponding to the impulse response of the channel from the plurality of samples.
2. The method of claim 1, in which the training signal comprises m repetitions of the modulated training sequence, and further comprising:
sampling, in each of n correlators, the training signal k times per repetition of the modulated training sequence in the received training signal to produce m�n�k samples of the received training signal.
3. The method of claim 1, in which the sampling rate is at least ten times slower than the chip rate.
4. The method of claim 1, in which the sampling rate is equal to a symbol rate of the training sequence.
estimating equalizer coefficients from an equalizer training sequence consisting of radio pulses.
estimating weights for the corresponding correlators to acquire most of the available energy of a data signal received via the channel, in which the data signal consists of ultra wide bandwith radio pulses.
7. The method of claim 1, in which a first subset of the plurality of samples are used for a rough estimate of the impulse response of the channel, and a second subset of the plurality of samples are used for an accurate estimate of the impulse response of the channel based on the rough estimate.
8. The method of claim 1, in which the estimate of the impulse response of the channel is based on a previous estimate of the impulse response of the channel.
9. The method of claim 2, where k is greater than one.
10. The method of claim 3, in which the chip rate is on the order of 10 GHz.
11. The method of claim 7, in which the second subset of the plurality of samples are obtained from training sequences received after obtaining the first subset of the plurality of samples.
12. The method of claim 2, where k is equal to one. Description
CROSS-REFERENCE TO RELATED APPLICATIONS A claim of priority is made to U.S. Provisional Patent Application Ser. No. 60/451,528, filed Mar. 3, 2003, entitled �Channel Estimation and Equalizer Coefficient Estimation for UWB Radio Communication Systems.�
FIELD OF THE INVENTION The present invention relates generally to radio communication systems, and more particularly to channel and equalization estimation in an ultra wide bandwidth communications systems.
BACKGROUND OF THE INVENTION With the release of the �First Report and Order,� Feb. 14, 2002, by the Federal Communications Commission (FCC), interest in ultra wide bandwidth (UWB) communication systems has increased. The IEEE 802.15 standards organization, which is responsible for Personal Area Networks, has established a task group, TG3a, to standardize a high-data-rate physical layer based on UWB.
Ultra wide bandwidth (UWB) communication systems transmit and receive extremely short electromagnetic energy impulses, therefore the terms �UWB� and �impulse radio� are used synonymously herein. Because the bandwidth of the pulses is much wider than the bandwidth of the payload signal, UWB is a form of spread-spectrum communication. Each pulse can cover anywhere from 500 MHz to several GHz of the radio spectrum.
Information is transmitted by modulating the frequency, timing, amplitude, polarity, or other aspect of the pulses. UWB systems can provide very high data rates for short-range wireless communications. In part, UWB systems are designed to distribute information in home, office, school, and industrial environments using high-speed links between computer devices.
However, it is a challenge to realize UWB modulation schemes that increase data throughput while minimizing errors in dense multi-path environments. Propagation measurements and channel modeling studies indicate that many multi-path components (MPCs) are expected for an UWB radio link. In a dense multi-path environment, the number of MPCs increases linearly with the bandwidth.
For example, a system with a 10 GHz bandwidth, operating in an environment with a maximum excess delay spread of 100 ns requires a thousand fingers in a rake receiver. Even in a sparse multi-path environment, like the channels specified by the IEEE 802.15.3a standard for channel models, up to 80 fingers are required to collect 80% of the available energy.
In order to collect most of the available energy from MPCs, while at the same time reducing the number of fingers in the rake receiver, it is desired to estimate the channel impulse response so that the correct reference waveforms for convolutions with the received signal at each rake finger can be determined.
The requirements for channel estimation in the IEEE 802.15.3a standard for data format are stringent. Data are to be transmitted in blocks of 8,000 bits. It is also assumed that the channel can change from block to block. Each block of data lasts only 0.1 ms. The typical speed of movement in an indoor environment is about 1 meter per second, so for a 10 GHz upper frequency limit, the maximum Doppler frequency is 30 Hz. Thus, the channel stays stationary for only 30 ms.
The impulse responses can last up to 200 ns, as can be seen in the Final Report and Order. Because sampling has to be done at a rate of about 10 G samples per second, this means that 2000 samples of the channel impulse response have to be evaluated. If data are transmitted in a constant stream, then is should be possible to exploit the correlation between channel realizations.
In the prior art, the channel impulse response and equalizer coefficient are usually estimated from a single pseudo-noise (PN) training sequence. However, other users and out-of-band interferers might be transmitting while the single training sequence is transmitted. Therefore, there is a need to suppress co-channel interferers. This can be done by spreading the training sequence.
A brute-force approach samples and A/D converts the measured impulse response at a speed of 10 G samples per second. In principle, the channel sounding requires only two microseconds, i.e., the length of the impulse response times a factor of 10 for the interference suppression, which is 200 symbol durations. This is much shorter than the duration of the data block, and thus is not a significant overhead. However, A/D converters that can process 10,000,000,000 samples per second are prohibitively expensive.
During the estimation period, while the single training sequence is transmitted, it is necessary to sample the received signal at a chip rate to find the delays and amplitudes of the received multi-path components. Because the number of MPCs is not yet known at this time, each possible resolvable delay, i.e., each chip period, must be estimated. For a 10 GHz system, that again means sampling and A/D converting at 10 G samples/s, which is prohibitively expensive.
Therefore, there is a need for method and system that can estimate the channel impulse response and equalizer coefficient at a lower cost without degrading performance.
SUMMARY OF THE INVENTION It is an object of the invention to provide a low cost channel estimator that can estimate the channel impulse response and equalizer coefficients in an ultra wide bandwidth (UWB) communications system.
According to the present invention, multiple training sequences are transmitted. Each training sequence includes, for example, fifteen symbols, and the training sequence is repeated, for example, fourteen times to suppress interference. There is a guard interval between two consecutive training sequences to avoid inter-sequence interference. Each symbol is �spread� over the spectrum by a predetermined sequence of chips at a chip rate.
After front-end processing, the UWB signal of the training sequences is passed to a rake-like receiver structure with a small number of parallel correlators (fingers), for example, three, for channel impulse response estimation.
The fingers sample each received training sequence, in parallel, with different time offset to produce samples. The samples substantially span the entire time interval of the impulse response. If the training sequence is repeated, then the samples have a fine resolution, and the channel impulse response can be estimated from the transmitted signal and the samples.
After the channel has been estimated, the weights for the rake receiver used for the data reception are determined. Finally, equalizer coefficients are estimated by minimizing the error between equalized outputs and the equalizer training sequence.
BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a detailed block diagram of a receiver with channel impulse response and equalizer coefficients estimation according to the invention;
FIG. 2 is a timing diagram of multiple training sequences according to the invention;
FIG. 3 is a flow diagram of a method for the estimating according to the invention;
FIG. 4 is a graph comparing results obtained by the estimating according to the invention;
FIG. 5A is a graph showing bit error rates;
FIG. 5B is a graph showing normalized mean-square errors;
FIG. 6 is a block diagram of a UWB system according to the invention; and
FIG. 7 is a block diagram of a UWB receiver according to the invention; and
FIG. 8 is timing diagram of rough and accurate estimates of an impulse response according to the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT System Structure and Operation
FIG. 6 shows a UWB system according to the invention. The system includes a transmitter 601 and a rake-like receiver 100 connected via a wireless channel 603. Both the transmitter and the receiver include a clock (CLCK) 604. The clocks are synchronized 605 to each other. The details of how this is achieved can vary, see, e.g., Meyr et al., Synchronization, Channel Estimation, and Signal Processing, Volume 2, Digital Communication Receivers, Wiley, 1997. The transmitter sends m training sequences 200 as described in detail below. The pulses of the training sequences are modulated at a chip rate.
As shown in FIG. 7, each of the m training sequences 200 is passed, in parallel, through multiple correlators 701 (rake fingers) of the receiver 100. Parallel �sample and hold� circuits 702 sample each received training circuits at multiple delay points with fixed offsets to obtain at least one (k=1) sample for each training sequence. It should be noted that each of the n fingers can also obtain serially more samples (k>1). Thus, the total number of samples can be expressed as (m�n�k). The idea is that these samples span a time interval corresponding to the impulse response at a resolution that is substantially equal to the chip rate.
However, the actual sampling rate according to the invention is at a substantially lower rate then the prior art sampling at the chip rate (on the order of 10 GHz) because the sampling extends over a longer period of time of the multiple training sequences. In fact, the sampling rate can be at the symbol rate (110 MHz in an 802.15.3a system). It should be understood that the sampling can also be at other low sampling rates. Thus, low cost components can be used for the receiver according to the invention, and the primary object of the invention is achieved.
After the sampling, the analog signal is AID converted 703 to a digital signal. The (m�n�k) digital signals from the fingers are further processed 705 to determine the channel impulse response.
In a second, optional, step, the estimate of the channel impulse response is then used to determine the weights of the rake receiver. For the basic prior art method see Molisch, Wideband Wireless Digital Communications, Prentice-Hall, 2001.
The rake coefficients are then used to weigh the output of the correlators 701 so that most of the available energy of the signal can be acquired. Thus, the invention estimates an �effective channel� from the antenna of the transmitter to the output of the summation device. Optionally, additional training sequences can be sampled at the symbol rate to provide an estimate of the channel impulse response of the effective channel, which, in turn, is the basis for the determination of the coefficients of an equalizer. The low rate samples are thus used to determine a full-resolution impulse response of the channel, and equalizer coefficients for the receiver. All of this is now described in greater detail.
In the transmitter, symbols are generated at a symbol rate 1/Ts. Transmitted pulses p corresponding the symbols are in the form of a Gaussian function
p  ( t ) = K 1  ⅇ - t 2 2  σ 2 , whose Fourier transform is
P  ( ω ) = K 2  ⅇ - σ 2  ω 2 2 . In this example, the variance σ2 is determined by
∫ - 2  π   f o 2  π   f o   P  ( ω )  2   ⅆ ω ∫ - ∞ ∞   P  ( ω )  2   ⅆ ω , where f is the frequency. From p(t), the spreading waveform can be obtained by
w  ( t ) = ∑ k = 0 N f   s k  p  ( t - kT c ) , where 1/Tc is the chip rate, which is substantially faster than the symbol rate. An example spreading sequence is {sk}={−1−1−1+1+1−1+1+1}. If the symbol sequence to be transmitted is {bk}, then the transmitted signal can be expressed as
s  ( t ) = ∑ k = - ∞ ∞   b k  w  ( t - kT s ) . Detailed Receiver Structure
FIG. 1 shows the rake-like receiver 100 according to the invention in greater detail. The receiver includes a conventional front-end 101 and three fingers 110 to acquire most of the available energy of a received signal 102. Each finger 110 includes a multiplier and low-pass filter 111, a programmable training pulse generator 112. These comprise the correlators 701 and sample and hold circuits 702 of FIG. 7.
Adjustable weight blocks 113 operate on digital signals 114. For clarity the details of the sampling and A/D circuits of Figure are not shown here. The digital signal is functionally related to a product of the output of the front end and the output of the programmable pulse generator.
The receiver also includes a timing controller 140 for the programmable training pulse generators 112. A channel estimator 150 provides input for the timing controller and an estimate 151 of the channel impulse response, which is used by the timing controller 140. A weight controller 155 adjusts the weights of the weight blocks 113 of each finger according to the estimated channel impulse response. An equalizer (EQ) training sequence generator 160 generates an equalizer training sequence 161 for an equalizer estimator 170 that produces coefficients 171 for a three-tap equalizer 130. The receiver produces output 131 is also fed back to the equalizer estimator.
After summing 120, a combined output 121 can be expressed as
x  [ n ] =  ∑ k = 0 3   γ n k *  ∫ s  ( nT s + τ + n k  Δ )  w *  ( τ )  ⅆ τ =  ∑ k = 0 3   γ n k *  r  ( nT s + n k  Δ ) , , where r(t)=∫s(t+τ)w*(τ)dτ, λk is the impulse response of the channel at n0Δ, where Δ is a minimum timing offset between two fingers.
To acquire as most of the available energy, we select {n1, n2, n3} such that {γn 1 , γn 2 , γn 3 } correspond to the three taps with largest energy magnitudes.
The three-tap linear equalizer 130 is used to mitigate residual inter-symbol-interference (ISI). If the coefficients of the equalizer are {c−1, c0, c1}, then the equalizer output 131 is
b ~ n = ∑ k = - 1 1   c k  x  [ n - k ] . To optimize performance, the equalizer coefficients 171 are selected to minimize a mean square-error of its output, that is
MSE=E|{tilde over (b)} n −b n|2.
Channel Estimation and Equalizer Coefficient Estimation
FIG. 2 shows the structure of the m pseudo-noise (PN) training sequences 200 according to the invention. Each of the multiple training sequences uses fifteen symbols 201-215. Each symbol is 75 nsec in duration, followed by a guard interval of 125 usec, for a total of 1250 nsec. If the sequence is repeated fourteen times 211-224, then the channel coefficients can be estimated in 17.5 μsec 250, followed by 2.5 μsec 270 for equalizer coefficients estimation, for a total of 20 μsec. The sequences can be the same or different.
Each training sequences are sampled, in parallel, at a symbol rate (1/Ts). During each symbol period, we observe at least n samples, e.g., three if there are three fingers. Because we need to estimate the entire impulse response at a resolution of the chip rate, we need forty samples during the symbol interval. Therefore, we repeat the training sequence fourteen (40/3) times. The timing offset of each finger can be adjusted by the controller 140 so that the output of each finger is as indicated in Table A below.
r(40nΔ)
r(40nΔ + 14Δ)
r(40nΔ + 28Δ)
r(40nΔ + Δ)
r(40nΔ + 15Δ)
r(40nΔ + 29Δ)
r(40nΔ + 2Δ)
r(40nΔ + 16Δ)
r(40nΔ + 30Δ)
r(40nΔ + 3Δ)
r(40nΔ + 17Δ)
r(40nΔ + 31Δ)
r(40nΔ + 4Δ)
r(40nΔ + 18Δ)
r(40nΔ + 32Δ)
r(40nΔ + 5Δ)
r(40nΔ + 19Δ)
r(40nΔ + 33Δ)
r(40nΔ + 6Δ)
r(40nΔ + 20Δ)
r(40nΔ + 34Δ)
r(40nΔ + 7Δ)
r(40nΔ + 21Δ)
r(40nΔ + 35Δ)
r(40nΔ + 8Δ)
r(40nΔ + 22Δ)
r(40nΔ + 36Δ)
r(40nΔ + 9Δ)
r(40nΔ + 23Δ)
r(40nΔ + 37Δ)
r(40nΔ + 10Δ)
r(40nΔ + 24Δ)
r(40nΔ + 38Δ)
r(40nΔ + 11Δ)
r(40nΔ + 25Δ)
r(40nΔ + 39Δ)
r(40nΔ + 12Δ)
r(40nΔ + 26Δ)
r(40nΔ + 13Δ)
r(40nΔ + 27Δ)
If the training sequence btk 's for k=0, 1, . . . , 14, then the training sequence can be expressed as
st  ( t ) = ∑ k = 0 14   bt k  w  ( t - kT s ) , and the channel output is xt(t)=h(t)*st(t)+nt), where h(t) is the channel's impulse response and n(t) is additive white Gaussian noise.
The Δ-sampled output of each correlator is r(nΔ)=∫xt(nΔ+τ)st*(τ)dτ. If the training sequence st(t) is white, then the channel parameters can be estimated by
h  ( n   Δ ) ≈ r  ( n   Δ )  st  ( t )  2 . However, st(t) is not perfectly white. Therefore, we modify the above estimation by the following discrete Fourier transform (DFT) steps:
1) Find the DFT of h(nΔ), Hk=DFT{h(nΔ)}. 2) Find the DFT of st(t), Stk=DFT{st(nΔ)}. 3) Modify the DFT of h(nΔ) by i. H ^ k = H k  St k  2 + ρ 2 4) Find the modified channel estimation by ĥ(nΔ)=I−DFT{Hk}.
Improved Channel Estimation
Because the channel impulse response is correlated for the sub-channels, the estimation of the channel impulse response can be improved, as shown in FIG. 3. For the first few, e.g., two, training sequences, set the timing offsets of the rake fingers of different sub-channels for rough channel estimation 310. This locates the portions of the impulse response that contain most of the available energy. Identify 320 the largest (six) taps according to the rough channel estimation. That is, set the offset timing so as to only sample near the rough estimates, instead of over the entire span of the impulse response. Then, estimate 340 the impulse response more accurately using another four training periods or 5000 nsec, and identify 350 the largest three taps from the six taps for the rake receiver and channel equalization.
As shown in FIG. 8, the rough estimates 801 for an impulse response 800, are used as a basis for the accurate estimates 802. Obviously, the rough to accurate refinement can be done in any number of steps.
It should be noted that more then one sample can be acquired concurrently by each rake finger for each training sequence. For example, if k (two or more) samples are taken at different time offsets, for each sequence, then the number of required sequences can reduced.
This simplified estimator only needs six training sequences instead of fourteen, which only requires 7500 nsec. Together with another 2500 nsec for equalizer coefficient estimation, the overall simplified estimation takes is only 10 usec, which is half the time required to estimate the channel from fourteen sequences.
It should also be noted, that the channel is re-estimated for each transmitted block. If the channel is slow-varying, a previous estimate can be used as a starting point for a next estimate to further reduce the required time.
Equalization Coefficient Estimation
After the impulse response is estimated, the rake receiver can be used to acquire most of the available energy of the received signal, and to mitigate the residual ISI. Therefore, after processing the training sequences for channel estimation, another training sequence is sent for equalizer coefficient estimation.
If the output of the rake receiver is x[n] when the training sequence is ckk., then the equalizer coefficients can be estimated by minimizing
1 31  ∑ n = 0 30   ∑ k = - 1 1  c k  x  [ n - k ] - ct n  . Consequently
( c - 1 c 0 c 1 ) = ( 1 31  ∑ k = 0 30  x -> k *  x -> k T ) - 1  ( 1 31  ∑ k = 0 30  x -> k T  ct k ) , where
x -> n = ( x  [ n + 1 ] x  [ n ] x  [ n - 1 ] ) . FIG. 4 shows results for the channel estimation according to the invention. When the SNR is below 0 dB, the normalized MSE (NMSE) of channel estimation decreases with an increase of the SNR. However, when SNR is above 0 dB, the NMSE has a floor, which is because training signal is not exciting enough.
The modified approach can significantly improve estimation performance. It can improve NMSE of overall channel estimation (whole) by 2 dB and NMSE of the three greatest taps (3-GT) by 2.6 dB.
For the three-tap equalizer output according to the invention, FIG. 5A shows the bit error rate (BER), and FIG. 5A shows the normalized NMSEe. For a 1% BER, the required SNR is about −2.5 dB.
Patent CitationsCited PatentFiling datePublication dateApplicantTitleUS5648983 *Apr 24, 1995Jul 15, 1997Lucent Technologies Inc.CDMA rake receiver with sub-chip resolutionUS6215814 *May 15, 2000Apr 10, 2001Nokia Networks OyRAKE receiverUS6266365 *May 17, 2000Jul 24, 2001Oki Techno CentreCDMA receiverUS6442193 *Mar 30, 1999Aug 27, 2002Koninklijke Philips Electronics N.V.Combining sub-chip resolution samples in arms of a spread-spectrum rake receiverUS6456647 *Dec 16, 1998Sep 24, 2002Lsi Logic CorporationTwo step signal recovery scheme for a receiverUS6570918 *Aug 19, 1999May 27, 2003Siemens AktiengesellschaftReceiver and method for recovering data from spread spectrum radio signalsUS6853689 *May 19, 2000Feb 8, 2005Telefonaktiebolaget Lm EricssonMethod and apparatus for channel estimation with transmit diversityUS6856646 *Mar 19, 2002Feb 15, 2005Nokia CorporationT-spaced equalization for 1xEV systemsUS7079604 *Oct 10, 2000Jul 18, 2006Freescale Semiconductor, Inc.Ultrawide bandwidth system and method for fast synchronization using multiple detection armsUS7116998 *May 14, 2003Oct 3, 2006Telefonaktiebolaget L M Ericsson (Publ)Subtractive multipath delay detectionUS7248622 *Jul 11, 2003Jul 24, 2007Stmicroelectronics Asia Pacific Pte. Ltd.Low-power code division multiple access receiverUS20020191568 *Oct 15, 2001Dec 19, 2002Koninklijke Philips Electronics N.V.Adaptive chip equalizers for synchronous DS-CDMA systems with pilot sequencesUS20030227961 *Jan 2, 2003Dec 11, 2003Anuj BatraRake receiver architecture for an ultra-wideband (UWB) receiverUS20030232612 *Jun 14, 2002Dec 18, 2003Richards James L.Method and apparatus for converting RF signals to basebandUS20040097204 *Nov 13, 2003May 20, 2004Peter JungMulti-subscriber detection using a rake receiver structureUS20040141559 *Oct 24, 2003Jul 22, 2004Tewfik Ahmed H.Generating UWB-OFDM signal using sigma-delta modulatorUS20070183535 *Oct 7, 2003Aug 9, 2007Irena MaravicSampling method for a spread spectrum communication system* Cited by examinerNon-Patent CitationsReference1 *Namgoong "A Channelized DSSS Ultra-Wideband Receiver" IEEE 2001.2 *Won Namgoong "A Channelized DSSS Ultra-Wideband Receiver", IEEE 2001.* Cited by examinerReferenced byCiting PatentFiling datePublication dateApplicantTitleUS7664163 *Nov 29, 2005Feb 16, 2010Renesas Technology Corp.ReceiverUS7756481 *Mar 25, 2009Jul 13, 2010Agere Systems Inc.Rake receiver with time-shared fingersUS8265122 *Dec 29, 2009Sep 11, 2012Renesas Electronics CorporationReceiverUS8422544Sep 17, 2007Apr 16, 2013Qualcomm IncorporatedCommunication receiver with an adaptive equalizerUS8615200 *Sep 23, 2010Dec 24, 2013Qualcomm IncorporatedSystems and methods for improving channel estimationUS20100103986 *Dec 29, 2009Apr 29, 2010Renesas Technology CorpReceiverUS20110013686 *Sep 23, 2010Jan 20, 2011Qualcomm IncorporatedSystems and methods for improving channel estimation* Cited by examinerClassifications U.S. Classification375/343, 375/349, 375/229, 375/136, 375/239, 375/340International ClassificationH04L27/06, H04L25/02, H04B1/00, H04L25/03, H04B1/69, H04L1/20Cooperative ClassificationH04B1/719, H04B1/709, H04L1/20, H04L2025/03484, H04B1/71637, H04L25/03012, H04L25/0226, H04L25/0212European ClassificationH04B1/719, H04B1/7163E, H04L25/02C3, H04L25/02C7A, H04L1/20, H04L25/03B1Legal EventsDateCodeEventDescriptionSep 22, 2011FPAYFee paymentYear of fee payment: 4Jul 10, 2003ASAssignmentOwner name: MITSUBISHI ELECTRIC RESEARCH LABORATORIES, INC., MFree format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:MOLISCH, ANDREAS;ZHANG, JINYUN;REEL/FRAME:014270/0147;SIGNING DATES FROM 20030709 TO 20030710RotateOriginal ImageGoogle Home - Sitemap - USPTO Bulk Downloads - Privacy Policy - Terms of Service - About Google Patents - Send FeedbackData provided by IFI CLAIMS Patent Services©2012 Google

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text: +The following abstracts and copies of original records may be accessed through online sources, the [[The Family History Library|Family History Library]] or the [http://www.ilsos.gov/GenealogyMWeb/iradsrch.html Illinois Regional Archives Depository (IRAD)] located at the Western Illinois University (WIU) - search for Schuyler County records. For information on how to use IRAD see the [[IRAD - Western Illinois University|WIU IRAD Wiki page.]] '''Copies of original records''' '''Copies of original records''' Line 180:


text:
sorting - Why is max slower than sort in Python? - Stack Overflow
I've found that max is slower than the sort function in Python 2 and 3.
$ python -m timeit -s 'import random;a=range(10000);random.shuffle(a)' 'a.sort();a[-1]'
1000 loops, best of 3: 239 usec per loop
$ python -m timeit -s 'import random;a=range(10000);random.shuffle(a)' 'max(a)'
1000 loops, best of 3: 342 usec per loop
$ python3 -m timeit -s 'import random;a=list(range(10000));random.shuffle(a)' 'a.sort();a[-1]'
1000 loops, best of 3: 252 usec per loop
$ python3 -m timeit -s 'import random;a=list(range(10000));random.shuffle(a)' 'max(a)'
1000 loops, best of 3: 371 usec per loop
Why is max (O(n)) slower than the sort function (O(nlogn))?
python sorting max python-internals share|improve this question edited Feb 23 at 14:50
You ran the Python 2 analysis once and the Python 3 code is exactly the same.
Jan 26 at 13:32
a.sort() works inplace. Try sorted(a)
@erip I fixed it
@Pretzel OP means the post has been edited, not that the problem has been fixed.
@WeizhongTu but sort sorts, and then a is sorted forever
You have to be very careful when using the timeit module in Python.
python -m timeit -s 'import random;a=range(10000);random.shuffle(a)' 'a.sort();a[-1]'
Here the initialisation code runs once to produce a randomised array a. Then the rest of the code is run several times. The first time it sorts the array, but every other time you are calling the sort method on an already sorted array. Only the fastest time is returned, so you are actually timing how long it takes Python to sort an already sorted array.
Part of Python's sort algorithm is to detect when the array is already partly or completely sorted. When completely sorted it simply has to scan once through the array to detect this and then it stops.
If instead you tried:
python -m timeit -s 'import random;a=range(100000);random.shuffle(a)' 'sorted(a)[-1]'
then the sort happens on every timing loop and you can see that the time for sorting an array is indeed much longer than to just find the maximum value.
Edit: @skyking's answer explains the part I left unexplained: a.sort() knows it is working on a list so can directly access the elements. max(a) works on any arbitrary iterable so has to use generic iteration.
38k64391
Good catch. I never realised that the interpreter state is retained across the code runs. Now I wonder how many faulty benchmarks I produced in the past. :-}
That much was obvious to me. But notice that even if you sort an already sorted array you have to check all the elements. Which is just as much work as getting the max.... To me this looks like a half-answer.
@KarolyHorvath, you are correct. I think @skyking got the other half of the answer: a.sort() knows it is working on a list so can directly access the elements. max(a) works on an arbitrary sequence to has ot use generic iteration.
Jan 26 at 13:45
@KarolyHorvath maybe branch prediction can explain why repeatedly sorting a sorted array is faster: stackoverflow.com/a/11227902/4600
@JuniorCompressor listsort.txt explains "It has supernatural performance on many kinds of partially ordered arrays (less than lg(N!) comparisons needed, and as few as N-1)" and then goes on to explain all kinds of gory optimizations. I suppose it can make a lot of assumptions which max can't, i.e. sorting is not asymptotically faster.
Jan 26 at 13:49
First off, note that max() uses the iterator protocol, while list.sort() uses ad-hoc code. Clearly, using an iterator is an important overhead, that's why you are observing that difference in timings.
However, apart from that, your tests are not fair. You are running a.sort() on the same list more than once. The algorithm used by Python is specifically designed to be fast for already (partially) sorted data. Your tests are saying that the algorithm is doing its job well.
These are fair tests:
$ python3 -m timeit -s 'import random;a=list(range(10000));random.shuffle(a)' 'max(a[:])'
1000 loops, best of 3: 227 usec per loop
$ python3 -m timeit -s 'import random;a=list(range(10000));random.shuffle(a)' 'a[:].sort()'
100 loops, best of 3: 2.28 msec per loop
Here I'm creating a copy of the list every time. As you can see, the order of magnitude of the results are different: micro- vs milliseconds, as we would expect.
And remember: big-Oh specifies an upper bound! The lower bound for Python's sorting algorithm is Ω(n). Being O(n log n) does not automatically imply that every run takes a time proportional to n log n. It does not even imply that it needs to be slower than a O(n) algorithm, but that's another story. What's important to understand is that in some favorable cases, an O(n log n) algorithm may run in O(n) time or less.
share|improve this answer edited Jan 26 at 14:02
answered Jan 26 at 13:50
This is the complete answer in one post, while the other two highly voted ones focus only on parts of the discrepancy.
This could be because l.sort is a member of list while max is a generic function. This means that l.sort can rely on the internal representation of list while max will have to go through generic iterator protocol.
This makes that each element fetch for l.sort is faster than each element fetch that max does.
I assume that if you instead use sorted(a) you will get the result slower than max(a).
7,297932
– JuniorCompressor
That assumption is only a one-liner-timing away to becoming more concrete. Not questioning your knowledge, just that such an addition is trivial for the demonstration of those who don't know it.
Not the answer you're looking for?	Browse other questions tagged python sorting max python-internals or ask your own question.	asked

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Celeste Simmons (#47318155)	member for 4 years, 11 months, 23 days
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Search Contributor's Records First NameLast NameVirtual CemeteriesMy Relatives (174)Find A Grave FriendsA AAA American ..., Barbara Anne (B..., CajunPaul, Herald, J L Bryant, jonesbitt, Lee Manning, Melissa Daigle, Oscar M. Clark, Superkentman, William Nees, WillieMessages left for Celeste Simmons (352)[Leave Message]
Vikki PruddenMathew Kennedy #93000705Thank you for the transfer.Added by Vikki Prudden on Jun 16, 2015 7:43 PMVikki PruddenMathew Kennedy #93000705Added by Vikki Prudden on Jun 16, 2015 7:43 PMTammy SatterRE: Thomas HavensHi, I do not know where he is buried. I noticed that there were a lot of Havens in the Decker-Union Cemetery. Have all the graves been identified? He was born July 19, 1768 according to the LDS. Thank you for getting back to me. TammyAdded by Tammy Satter on Jun 16, 2015 9:07 AMTammy SatterThomas HavensHi,I am looking for the grave of Thomas Havens who was married to Mary Chamberlain. It is possible that his first name was different. People of German/Dutch descent often did that. He died between 1826-1836. Do you think he may be buried here? Thank you. Tammy Hill SatterAdded by Tammy Satter on Jun 11, 2015 6:14 PMM K IIHas the snow melted yet?Hello From Idaho, Thank you for being such a big contributor to this site! If you find your self in Summit, NJ and have time to take photos...my headstone photo request is in St. Teresa Cemetery. My grandparents and aunt & uncle. All Walsh's. Block 9, Section K, Plot 1 & 2. John, Jean (Russell), John, Norma (Karn)-all Walsh. If not, I will keep searching for another North Jersey Photographer. :)MK IIAdded by M K II on May 28, 2015 10:22 AMJacqueline Wells LubinskiBarbara GonzolThank you for taking the picture of the stone for Barbara Gonzol. She was my mom's baby sister who died as an infant.Added by Jacqueline Wells Lubinski on May 11, 2015 7:23 PMjeff coxRE: Pellett stoneThanks for the reply Celeste, good to know...- JeffAdded by jeff cox on Apr 23, 2015 4:16 PMMary Lou PfenningNoah DaytonBuried in Anderson Cemetery in Lagrange County Indiana. We are trying to find any Veterans that may have served in the War of 1812. Anyone that may have any information on Noah would be greatly appreciated.Mary Lou PfenningAdded by Mary Lou Pfenning on Apr 22, 2015 6:34 PMjeff coxPellett stoneLooks like the picture you have for Obidiah Pellett is for possibly his son as the dates do not match the memorial.Find A Grave Memorial# 14534427- JeffAdded by jeff cox on Apr 19, 2015 3:32 AMReeTDuplicate MemorialsFYI Your memorial #93195907 for Kezia Westervelt Hopper should be deleted as an early memorial for her #16479217 exists. Thanks, ReeAdded by ReeT on Apr 18, 2015 9:10 PM[View all messages...] Privacy Statement and Terms of Service Advertisement

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