Hallo!
Wait, (a+b*i) = frequency? If so that makes more sense as to why even
hm, frequency ... the bins are the frequencies. If you have e.g. a FFT size of 1024 you will get 1024 different frequencies (well, 512, because the other half is the negative spectrum ...) e.g. 44100/1024 = 43, so the first sample of the 1024-block out of the fft will give you a and b (or r and phi = Magnitude and Phase) of the frequencies from 0 to 43 Hz (this is the first bin), the next bin is 43 to 86 Hz and so on ...
that to mean more then just frequency. For example in the xy plane if you add two vectors you don't neccessarily just get a y value back.
how do you add 2 vectors and don't get a y value ?
Multiplication in the frequency domain involves frequency magnitude, but also frequency phase and frequency value. It seems to me that frequency space is 3D where as time space is 2D also.
I don't understand what you mean with frequency value, both time and frequency space can be real or complex ...
I think AM is only time domain...Having looked at www.dspguide.com the correct equations are, unlike the last thing I posted (sorry!):
ReY[f] = ReX[f]ReH[f] - ImX[f]ImH[f] ImY[f] = ImX[f]ReH[f] + ReX[f]ImH[f]
yes, that's what I wrote before: (a1 + b1*i)*(a2 + b2*i) = a1*a2 - b1*b2 + (a1*b2 + a2*b1)*i real imaginary
LG Georg