Re: [Alsa-user] multichannel multiband FFT-based equalizer - README

[fons a. <fon...@sk...>]

On Mon, Jan 02, 2006 at 11:37:54PM +0200, Sergei Steshenko wrote:

> So, how are going to implement a central frequency which is
> not a multiple of (Fs / N) in a DFT equalizer ?
> 
> That is, what data resulting from direct DFT represents such frequencies ?

A weighted sum of some DFT outputs, instead of just one of them.

Look at what you have now. You do a forward FFT and get N complex
values A [i]. You multiply each of these A [i] by some factor, and
then do an IFFT.

The second step can be regarded as the multiplication of the vector
A [i] by a diagonal matrix. Using central frequencies in between
the 'integer' bins would just mean this matrix is no longer diagonal.
In practice it would become a band matrix and still be quite sparse,
and the product can be done efficiently.

Once you have the matrix instead of the term by term product, the
windowing can also be absorbed into it.

-- 
FA