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

[Sergei S. <ste...@li...>]

Regarding

"A weighted sum of some DFT outputs"

- do you agree that if, say, I have an 8 point FFTW, the following
frequencies are represented in the FFTW output array C (the result of time ->
frequency conversion, i.e. direct FFT):

C[0]       <=> DC (only real part)
C[1], C[7] <=> 1 * Fs / 8;
C[2], C[6] <=> 2 * Fs / 8;
C[3], C[5] <=> 3 * Fs / 8;
C[4]       <=> 4 * Fs / 8; Nyquist frequency (only imaginary part)

?

If yes, do you agree that no SINGLE C-array element represents, say
1.5 * Fs / 8 frequency ?

If yes, do you agree that changing simultaneously gain of
C[1], C[7] and C[2], C[6] pairs. i.e of the pairs that represent
(1 * Fs / 8)  and (2 * Fs / 8) pairs I will not only change gain
of (1.5 * Fs / 8) frequency, but also of the whole
1 * Fs / 8) .. (2 * Fs / 8) frequency range ?

If yes, do you agree that had I wanted to change only gain of,
say, (2 * Fs / 8), i.e amplitude of (C[2], C[6]) I wouldn't have changed
the amplitude of, say, (1 * Fs / 8) spectral component or any other
spectral component for that matter ?

If yes, that's what I meant saying that central frequencies should
be a multiple of frequency resolution ((Fs / 8) in this example).

If central frequency is not a multiple of frequency resolution,
its amplitude can NOT be changed without affecting the amplitude
of other spectral components.


On Mon, 2 Jan 2006 23:53:33 +0100
fons adriaensen <fon...@sk...> wrote:

> 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
> 
> 
> 
> 
>