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I am interested in using Band Edge Filters to do carrier frequency recovery but this is kind of secondary to my question which is:

How do you build an FIR filter which isn't symmetric about the negative frequency axis?

From what I remember basic FIR filter design enforced conditions resulting in the filters always being symmetric.

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  • $\begingroup$ You remembering that is wrong. For example: take any symmetric FIR. Multiply point-wise with $e^{j\alpha n}, n=1,2,\ldots$. Almost all $\alpha$ will lead to non-symmetrical filters. $\endgroup$ – Marcus Müller Feb 8 at 10:02
  • $\begingroup$ I just reviewed the basic way to approximate filters using the L2 norm so I understand how to generate them(but they will be complex). $\endgroup$ – FourierFlux Feb 8 at 18:32
  • $\begingroup$ By the way, what is the frequency shift property of the dft and can this be used to shift a filters frequency response? I know how multiplying by a complex exponential shifts the spectrum by the frequency coefficient in continuous time domain. $\endgroup$ – FourierFlux Feb 8 at 18:33
  • $\begingroup$ yeah, so that's exactly it. Nothing more to it. $\endgroup$ – Marcus Müller Feb 8 at 18:35
  • $\begingroup$ Ok cool, do you have an intuitive explanation of the negative spectrum? Like what actually gets spit out of a filter which remove the positive spectrum of a signal? $\endgroup$ – FourierFlux Feb 8 at 18:47

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