Hallo, Chuckk Hubbard hat gesagt: // Chuckk Hubbard wrote:
Okay, I've read through some of the Fourier explanation in this Digital Filters book, and I think I understand. That was going to be one of my next questions: if the data of the FFT actually has the same number of possibilities as the audio data itself (by bit rate and block size), is there then a 1 to 1 relationship, where no two audio blocks could have the same FFT data. I take the answer to be yes. I was told by an electrical engineer that short block sizes miss lower frequencies, but that seems to be covered with the DC channel, even down to a block size of 4.
Well, it's a bit more complicated than that, you don't loose lower frequencies, you loose frequency resolution with smaller windows.
First, the true Fourier transform only is valid for "endless" periodic signals like additions of sine waves. There we have no information loss when transforming back and forth. But as we don't have infinite periodic signals in real world, windowing is used to make signals look as if they were infinite and periodic. But windowing changes the original signal (it's like amplitude modulation) and it limits the frequency resolution of the resulting spectrum. Assuming you use a window of 100 samples at a sample rate of 10,000 kHz. Then the fundamental frequency of your analysis will be 10,000/100 = 1000 Hz and you will only get harmonics between +/-Nyquist: -5000, -4000, ..., -1000, 0, 1000, ..., 5000.
Using a larger window, like 1000 samples, you get a finer resolution in steps of 10,000/1000 = 10 Hz: -5000, -4990, -4980, ..., 0, 10, 20, ..., 5000 however you loose temporal resolution, as you now have to wait 1000 samples instead of only 100 to detect changes in frequency content.
Ciao
Frank Barknecht _ ______footils.org_ __goto10.org__