Burg (1972) established an analytical relationship between maximum entropy and maximum likelihood spectral density estimates. If SE(f,j), j = 0, 1, … M − 1 and M successive maximum entropy spectral density estimates at frequency f, then the M-length maximum likelihood spectral density estimate SL(f,M) is given by
$1SL(f,M)=1M∑j=0M−11SE(f,j).$
The maximum entropy estimates are made via Burg's well-known formula,
$SE(f,N)=PNΔt|∑k=0NγkNe−i2πfkΔt|2,$
where γkN, k = 0, 1,…,N are the coefficients of the N-length prediction-error filter, PN is its error power, and Δt is the sample interval. These estimates can be recursively calculated as shown by Burg (Smylie et al, 1973).
This content is PDF only. Please click on the PDF icon to access.

### First Page Preview Close Modal
{"ft_lang_label":"__label__en","ft_lang_prob":0.8281247,"math_prob":0.99334294,"size":684,"snap":"2023-40-2023-50","text_gpt3_token_len":158,"char_repetition_ratio":0.1367647,"word_repetition_ratio":0.0,"special_character_ratio":0.23391813,"punctuation_ratio":0.14074074,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9966795,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,6,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-03T17:35:57Z\",\"WARC-Record-ID\":\"<urn:uuid:5f6abd00-a13e-4bb9-a9bb-cccbf144d351>\",\"Content-Length\":\"93543\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c4beab21-2eb3-4ccf-919b-47fa97ca1ae5>\",\"WARC-Concurrent-To\":\"<urn:uuid:824de18a-7e57-4add-ad20-6ce2f8f4e9ff>\",\"WARC-IP-Address\":\"52.224.196.54\",\"WARC-Target-URI\":\"https://pubs.geoscienceworld.org/geophysics/article-abstract/44/10/1738/68264/The-relationship-between-maximum-entropy-and?redirectedFrom=fulltext\",\"WARC-Payload-Digest\":\"sha1:C3STNCX5BKGAKUDZKJQZUD43F6JAFPOM\",\"WARC-Block-Digest\":\"sha1:YVBIGX3BB5OLWSJQECEB4H45UEKNKHOS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511170.92_warc_CC-MAIN-20231003160453-20231003190453-00378.warc.gz\"}"}