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I'd like to know if anyone has a proof of why the condition of symmetry or antisymmetry must be followed by a FIR filter, in order for it to have a linear phase response?

I've been pouring over this for an exam, and my initial question was what constitutes a linear phase response and after a little pouring and talking with myself I finally got that it is because of the [itex]\left|H\left(\omega\right)\right|[/itex]X[itex]\left(\omega\right)e^{-j\omega n_{0}}[/itex] that the x(n) will be delayed by n_0 samples.

Now, however, the only step I need to have rounded this off is a proof to myself that the impulse response of the filter must be symmetric in order for a linear phase response to occur.

Thank you in advance,

Rune

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# DSP - FIR Filters, linear phase conditions

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