# Band Edge Filters

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.

• 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. – Marcus Müller Feb 8 '19 at 10:02
• 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). – FourierFlux Feb 8 '19 at 18:32
• 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. – FourierFlux Feb 8 '19 at 18:33
• yeah, so that's exactly it. Nothing more to it. – Marcus Müller Feb 8 '19 at 18:35
• 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? – FourierFlux Feb 8 '19 at 18:47