While trying to do frequency domain filtering of audio signals using windowed overlap-add methodology, I came across some pre-calculated frequency domain coefficients. I noticed that the coefficients, complex numbers, are not conjugate symetric. Can that be? What does it tell me about the filter?
If the input filter is FIR, described by
y(n)=b(1)x(n)+b(2)x(n−1)+⋯+b(nb+1)x(n−nb), then the discrete Fourier transform of this real filter coefficients should be conjugate symetric as for any other real input. Furthermore, after the input signal is transformed to frequency domain, multiplied with the filter coefficients, and transformed back to time domain using inverse DFT, the signal (
audio_filtered) should again be real?
A = fft(audio); H = fft(filter); Afiltered = A .* H; audio_filtered = ifft(Afiltered)
If the input filter is IIR, are things different with respect to conjugate symetry?