I'm using a 4-pole elliptic BPF in my work. Related recursive equations are:
in = a0*c0 - a1*c1 - ...
out = b0*c0 + b1*c1 + ...
c1 = c0;
Output spectrum from the filter has 2 symmetric peaks: 1 @ omega +.2 and another at -.2, second one being slightly stronger. Input is asymmetric. Is the data in those 2 peaks the same? (input frequencies differ at those 2 points). Can I safely discard one of the 2? Better even can i just process the combined output, to save on 1 more FFT?
If by "input is asymmetric" you mean that the input signal is complex or in quadrature, then no, you can't discard one peak.
If the input signal is real, then all the information about the signal is carried in either the positive-frequency side or the negative-frequency side of the spectrum.
I should state more correctly that FFT of the input signal is asymmetric. It is complex and produced by quadrature ADC samplers. If it were just real, input FFT spectrum would be symmetric...
Just looking at the 2 peaks, the +2 is what I want, the -2 corresponds to the wrong frequencies. I am asking this here, because I don't know much about the derrivation of these constants. With filters at omega +.1, the second peak appears at -.1, with +.4/-.4, and so on, symmetric always about center frequency.
Does this happen always with these DSP filters? Could the data in those 2 peaks be mirrored?