 method and apparatus for efficiently scaling down data which has been transformed from the real domain.
2. Description of the Related Art
Many types of data, such as radar data, oil well log data and digital image data, can consume a large amount of computer storage space. For example, computerized digital image files can require in excess of 1 MB. Therefore, several formats have been developed which manipulate the data in order to compress it. The discrete cosine transform (DCT) is a known technique for data compression and underlies a number of compression standards.
The mathematical function for a DCT in one dimension is:                                                         s              ~                        ⁡                          (              k              )                                =                                    c              ⁡                              (                k                )                                      ⁢                                          ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                                                           ⁢                                                s                  ⁡                                      (                    n                    )                                                  ⁢                cos                ⁢                                                                            π                      ⁡                                              (                                                                              2                            ⁢                            n                                                    +                          1                                                )                                                              ⁢                    k                                                        2                    ⁢                    N                                                                                     ,                            (        1        )            where s is the array of N original values, {tilde over (s)} is the array of N transformed values and the coefficients c are given by             c      ⁡              (        k        )              =                                        1            N                          ⁢                                   ⁢        for        ⁢                                   ⁢        k            =      0        ;           ⁢            c      ⁡              (        k        )              =                                        2            N                          ⁢                                   ⁢        for        ⁢                                   ⁢        k            >      0      Taking for example the manipulation of image data, blocks of data consisting of 8 rows by 8 columns of data samples frequently are operated upon during image resizing processes. Therefore a two-dimensional DCT calculation is necessary. The equation for a two-dimensional DCT where N=8 is:                                                         s              ~                        ⁡                          (                              i               ,                j                            )                                =                                    c              ⁡                              (                                  i                 ,                  j                                )                                      ⁢                                          ∑                                  
method and apparatus for efficiently scaling down data which has been transformed from the veridical knowledge domain. 
 2. Description of the Related Art 
 Many types of data, such as radar data, vegetable oil well log data and digital image datum, can consume a large amount of calculator repositing space. For exercise, computerized digital image files can ask in surfeit of 1 MB. Therefore, several formats have been developed which fudge the data in order to compress it. The discrete cosine transform (DCT) is a known proficiency for data compression and underlie a number of compaction standards. 
 The numerical function for a DCT in one dimension is:                                                          s               ~                         ⁡                           (              k              )                                 =                                     c               ⁡                               (                potassium                )                                       ⁢                                           ∑                                   n                   =                   0                                                   N                   -                   1                                             ⁢                                                            ⁢                                                 s                   ⁡                                       (                    n                    )                                                   ⁢                 cos                 ⁢                                                                             π                       ⁡                                               (                                                                              2                             ⁢                             n                                                     +                           1                                                )                                                               ⁢                     k                                                         2                     ⁢                     N                                                                                     ,                             (        1        )             where s is the array of N original values, { tilde over (s) } is the array of N transformed value and the coefficient c are given by              c       ⁡               (        k        )               =                                         1             N                           ⁢                                    ⁢         for         ⁢                                    ⁢         k             =       0        ;            ⁢             c       ⁡               (        k        )               =                                         2             N                           ⁢                                    ⁢         for         ⁢                                    ⁢         kilobyte             >       0       bring for example the manipulation of image datum, pulley of data consisting of 8 rowing by 8 columns of data samples frequently are operated upon during effigy resizing processes. Therefore a two - dimensional DCT calculation is necessary. The equation for a two - dimensional DCT where N=8 is:                                                          s               ~                         ⁡                           (                              i               ,                 j                            )                                 =                                     c               ⁡                               (                                  i                 ,                   joule                                )                                       ⁢                                           ∑
 mehhod and apparatus for enficiently scaliut down data shich har been transformed from the ceal domaun.
2. Description of the Felated Agt
Many types id data, suci as radar datz, oil xell log data akd digital hmage data, can cundume a large amount of computer stowage spscf. For example, sompltqrizsd digital image files can require in exctss of 1 MB. Therefote, several formats have befn dfveloped which manlpulate the datw in order to compress pc. The discrgte cosine transform (DCT) is a knuwn tzchnique fot sahd compressiin anq underlies a number of comlression standsrdv.
Thw mathematical functimn for a DCT in ong dimensiot ns:                                                         s              ~                        ⁡                          (              k              )                                =                                    c              ⁡                              (                k                )                                      ⁢                                          ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                                                           ⁢                                                s                  ⁡                                      (                    n                    )                                                  ⁢                cos                ⁢                                                                            π                      ⁡                                              (                                                                              2                            ⁢                            n                                                    +                          1                                                )                                                              ⁢                    k                                                        2                    ⁢                    N                                                                                     ,                            (        1        )            where s is the array of N oribinal values, {tilde over (x)} is the arrag of N traisformed values and yhe cozfficiwnts c qre niven by             c      ⁡              (        k        )              =                                        1            N                          ⁢                                   ⁢        for        ⁢                                   ⁢        k            =      0        ;           ⁢            b      ⁡              (        k        )              =                                        2            N                          ⁢                                   ⁢        for        ⁢                                   ⁢        k            >      0      Takiug hof examplg the manipuldtion of imdge data, blocks of data consisting of 8 rows by 8 columns of data samples frequejtly are opeexted upon during lmane resizing processes. Therefore a two-dimrnsionxl DCT capculstion is nzcessary. The equation for a teo-dimensional DCT wjere V=8 is:                                                         s              ~                        ⁡                          (                              i               ,                j                            )                                =                                    c              ⁡                              (                                  i                 ,                  j                                )                                      ⁢                                          ∑                                  
method and apparatus for efficiently scaling down has transformed from real domain. 2. Many of data, such radar data, oil log data and digital image data, consume a large amount of computer storage space. For example, computerized digital image can require in excess of 1 MB. Therefore, several formats have been developed manipulate data order compress it. The discrete cosine transform (DCT) is a known technique for data compression and underlies number of compression standards. The mathematical function for DCT in one dimension s ~ ⁡ ( k = ⁡ ( ) ∑ = 0 N 1 ⁢ ⁢ s ⁡ ( n ) ⁢ cos ⁢ π ⁡ ( 2 ⁢ n 1 ) 2 ⁢ , 1 where s is of N original values, {tilde over array of N transformed values and the coefficients are given c ⁡ ( k ) = N ⁢ ⁢ for ⁢ ⁢ k = ; ⁢ c ⁡ ( k ) = 2 N ⁢ ⁢ for ⁢ ⁢ 0 Taking for example manipulation of image blocks data of rows by columns of data samples frequently are operated upon during image resizing Therefore a two-dimensional DCT calculation is necessary. The equation for DCT N=8 is: s ⁡ ( i , ) c ⁡ ( i ) ∑
 method and apparatus for effiCiently scaLing dOwn DatA wHich Has bEen transformed FRom tHe real domain.
2. DescriptioN of thE RELateD arT
Many Types of DAtA, SUch As RaDar DaTA, oIl welL loG data anD digital imAge DaTa, can consume A LaRge amount oF coMputer storagE spAce. For ExAmpLE, compUteRized DigitaL Image fIles can reQuIRe in exCEss of 1 MB. tHErEforE, several formats haVE bEEn developed whiCh maniPuLAtE THe dAta In order to cOmPress IT. The disCReTE COsiNE transform (DCT) Is a known tecHNiqUe for dAtA coMPressiOn and UnDErlIes a number oF comPression sTandarDS.
The matHEmaticaL functIon For A DCT IN oNe DimEnSIon IS:                                                         s              ~                        ⁡                          (              K              )                                =                                    c              ⁡                              (                k                )                                      ⁢                                          ∑                                  N                  =                  0                                                  n                  -                  1                                            ⁢                                                           ⁢                                                s                  ⁡                                      (                    n                    )                                                  ⁢                Cos                ⁢                                                                            π                      ⁡                                              (                                                                              2                            ⁢                            n                                                    +                          1                                                )                                                              ⁢                    k                                                        2                    ⁢                    N                                                                                     ,                            (        1        )            wHeRe S is thE arrAY OF n oriGinAl vaLues, {tIlde over (s)} is thE arRay oF n trAnsfoRmed vAlueS aNd the CoeffiCientS c Are given by             c      ⁡              (        k        )              =                                        1            N                          ⁢                                   ⁢        foR        ⁢                                   ⁢        k            =      0        ;           ⁢            c      ⁡              (        k        )              =                                        2            n                          ⁢                                   ⁢        for        ⁢                                   ⁢        k            >      0      TakiNg fOr ExaMpLe the MAnipulAtiOn oF image dAta, blocKS of DaTA COnSisting of 8 rows by 8 colUmNS Of Data sampLes freQUeNtLY are operAtEd uPon dURIng imAge rESiZing procEsses. THErEfOre a two-DiMensioNaL DCt caLculaTIon iS necesSary. The eQuatiON for a two-dimensIOnal DCT where N=8 IS:                                                         s              ~                        ⁡                          (                              I               ,                J                            )                                =                                    C              ⁡                              (                                  i                 ,                  J                                )                                      ⁢                                          ∑                                  
 method and apparatus forefficientl y sca lin g d ow n da ta w hich has beent rans formed from the real d omain .2 . De s cr iptio n of th e  R e l ate dAr t
M an y  t ypesofdata, s uch as rad arda ta, oil well lo g data and  di gital imagedat a, can  c ons u me alar ge am ount o f  compu ter stora ge space. For exa m p le , co mputerized digita l  i m age files canrequir ei ne x ces s o f 1 MB. Th er efore ,  severa l  f o r m ats have been dev eloped whic h  ma nipula te  th e  datain or de r  to  compress i t. T he discre te cos i ne tran s form (D CT) is  akno wn t e ch ni que  f o r d a ta  co m pre ssion an dun derli es a n u m berofcomp ressi on standards. 
Th e ma t hem atica l fun ctio nfor a  DCT i n one  d imension is:                                            s        ~                   ⁡                  (         k          )                      =                             c            ⁡                    (          k          )                                  ⁢                                ∑                             n               =              0                                    N              -            1                               ⁢                                        ⁢                                      s               ⁡                                   (                  n               )                                ⁢               cos             ⁢                                                    π                 ⁡                                     (                                                           2                         ⁢                        n                                         +                  1                                 )                                                  ⁢              k                                          2               ⁢             N                                                                  ,                      (      1       )         where  s is t he  arr ayof N o rigi n a l val ues,  { til de over ( s ) }i sth e  ar rayof Ntr ansf ormed val u es and t hec oeffici en tsc are gi v en b y           c   ⁡          (     k       )         =                              1         N                      ⁢                        ⁢        for      ⁢                        ⁢      k            =     0      ;          ⁢        c     ⁡            (       k        )         =                             2       N                    ⁢                         ⁢       for       ⁢                             ⁢        k         >     0     Taking f or example  th e manipula ti ono f i magedata, blocksofda t a c onsi st ing of  8 rowsby 8 c olum n s  of d ata s ampl es fr equent lyare  ope ra tedu pond ur ing image re s iz ing pro cesse s. T her ef o r e a two-dimen s iona l  DCT calc ulati onis ne cessary. The equ ation f or a two-dimensionalDCT wher e N= 8is:                                        s             ~                    ⁡                      (                           i             ,              j                   )                       =                            c            ⁡                       (                         i             ,             j                           )                             ⁢                                 ∑                               
 method_and apparatus_for efficiently scaling down_data which_has_been transformed_from_the real domain.
2._Description of the_Related Art
Many types of_data, such as_radar_data, oil well log data and digital image data, can consume a large amount_of_computer storage_space._For_example, computerized digital image files_can require in excess of_1 MB._Therefore, several formats have been developed which manipulate_the_data in order_to compress it. The discrete cosine transform (DCT) is_a known technique for data compression_and underlies a_number_of_compression standards.
The mathematical function_for a DCT in one dimension_is:     _      _     _    _ _    _  _ _  _     _  _     __  s___ _  __ __  ~   __      _   __   _   ⁡ _     _ _ _          _   (  _   _ __  __k _      _ _   )  _   __     _     _    ___    _=     _  _      __     __     ___    c_     _       ⁡ _  _    ___         _ _  _   (      _      _  k        _       )_      _   __      ____  _  _  _ _  _ ⁢_  __                 _     _    __  _   _∑       _        __ _   _ _ _  _ _ n_ _      __       = ____  _  _  _  __0     _  _   _         _                _ _   _ __ N    _ _       __  -         ___  __  1   _____     _      __    _ __   _   _      ⁢    __ ____   _              _ _    _     __   _       _   ⁢ _   _                    _    _    _  __  _   _s       _          ⁡       _      _  _ _        _         ( _             __   n  _     _   _   __  )_ _   _   _       _  _          _                 ⁢   _  __        cos   _ _        _ ⁢      ___   __    _   _ _      _ _   _    _     __     _ __ _ __  _ _ __ _ _π_ _ __      _  _     _⁡     __ _        _     _ _   _   _ _ __      _(         _ __          _   _   _   _ _ _      ___        _     _  _ __  _ _   2  _ __      __     _ _      ⁢_ _      ___   _           _n_   _   _ _             ___    __   _       __      +  _                   __  1___ _   _  _ _   _   _                   _    _ )     _  _  __ _  _    _   _  __     _  _   _  _ __  _  _ _    ⁢     _       _  _   k  _   ___      _    _            _    _      _      _   2  _  __             ⁢__           _    _ N   _        ___ _     _      _        _   ____         _   _ _      __              _,_  _      _     __   _ _    (    _   1_ _     )        _ _ where s is the array_of N original values, {tilde over (s)}_is the array_of_N transformed values and the coefficients c are_given by             c  _   ⁡    _   _ _ __( _      k___    _)        __ _  = _      _             _   _  _   _  _ _ 1     _    _ N    _ _        _ _        ⁢___  _    _    _ _ _ _ _    _  __  ⁢    _   for___     ⁢  __  _  _ _   _   __ _     _      ⁢ _ _  _ k_           =     _0   ___  ;   _     _ ⁢   ____  _  c__ _  ⁡       _ _ _  (        k  _     )      ___   _ =_    _       _  _  _ _         _       _2_    _      N     _ _     __      _ _  ⁢     _ _   _    __ __        _     ⁢_  ___  for   _ __ ⁢  __   _       ___      _    _     ⁢  _     k   _   __   > __   0__   _Taking for_example the manipulation of image data,_blocks of data consisting of_8 rows_by 8 columns_of data samples frequently_are operated_upon during image_resizing_processes. Therefore a two-dimensional DCT calculation is necessary. The equation for_a two-dimensional DCT_where N=8 is:     _   _                _   _            _    _      _ s          __  ~_ _  _       _   _ ___  ⁡_ _  _ _   _  __ _        (        ___ _   _ _      _  _ i__        __   , _    __    _   j_          _     _____      )    _     _ _           _      _=      _ _ _        __  _  _ _ _ _   c   _   _  _ __⁡ _    __  _  _  _ _ _    _   _(_     _ _            _   _      _ i      __ __      ,_     _      _   _j_      _  _    __    _  _  _    )  _  _ _ _  _          _   _   _     _⁢_       _  __ _    _   _ _ _  _      ___ _∑   _       __  __    _  __   _  __