On Tue, Jan 03, 2006 at 01:22:56AM +0200, Sergei Steshenko wrote: > - 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)
Yes, except that it's the cosine (real) part of Fs/2, that is in C[4]. > If yes, do you agree that no SINGLE C-array element represents, say > 1.5 * Fs / 8 frequency ? Yes. > 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 ? Yes. This is no different from changing only one value - it represents more than just the exact central frequency (you'd have a very bad equaliser otherwise !). The minimum bandwidth you can make is Fs/N, and a bit more with windowing. You may have some difficulty in believing that a 'non-integer' band could have the same bandwidth as an 'integer' one, but it *is* possible, and even quite straightforward. Look at it like this: there is no essential difference between the time and the frequency domains, they are 'duals'. Just as you can delay a sampled signal by half (or any fraction of) a sample by interpolation and without impairing bandwidth (i.e. resolution in the time domain), you can interpolate in the frequency domain without impairing resolution. The output of a DFT is just 'samples in the frequency domain', like the input is 'samples in the time domain'. Or one more variation: you say "no SINGLE C-array element represents, say 1.5 * Fs / 8 frequency", and that is correct. In the same way, in a sampled signal, no single sample represents the value of the original analog signal halfway between samples i and i+1. It is represented by all surrounding samples, with sin(x)/x weighting. And it can be reconstructed. The same is true in the frequency domain. -- FA ------------------------------------------------------- This SF.net email is sponsored by: Splunk Inc. Do you grep through log files for problems? Stop! Download the new AJAX search engine that makes searching your log files as easy as surfing the web. DOWNLOAD SPLUNK! http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click _______________________________________________ Alsa-user mailing list Alsa-user@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/alsa-user
