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In the A2DP specification, the SBC code uses a "polyphase filterbank" which has the formula $$x[n] = X[m]\cos((m+0.5)(n+M/2)\pi/M).$$ I am confused to what this is? It seems to take in $N$ points and output $2N$ points in some sort of frequency domain. Is this a special type of DFT and can it be optimized with a radix-2 algorithm? I tried searching but could not find any websites that could help me.

Edit: Links - https://www.bluetooth.org/docman/handlers/downloaddoc.ashx?doc_id=8236 and bottom of Page 64

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    $\begingroup$ Could you provide a link to the specification as well as the approximate position of this formula in the document so that we can get more context (you can edit your question) ? $\endgroup$
    – anpar
    Jun 12 '17 at 20:11
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I figured out the answer. The polyphase filterbank in the SBC codec is a variation on the discrete cosine transform type 4 that also divides it into frequency bands at the same time. If you look in the spec, the double for loop is used to both to multiple across all basis and sum up the frequency bands.

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  • $\begingroup$ You can "select" your answer to resolve this question. $\endgroup$
    – msm
    Jul 15 '17 at 6:28

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