# DSP - FIR Filters, linear phase conditions

1. Aug 22, 2012

### Runei

Hello there

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 $\left|H\left(\omega\right)\right|$X$\left(\omega\right)e^{-j\omega n_{0}}$ 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.