EE5410 signal Processing -- FIR : zero phase non-causal vs linear phase causal filter
1. from the symmetry properties of the Fourier transform of real signals, we know that ANY non-recursive filter with an impulse response that is REAL and EVEN with have a frequency response H(e^jw) that is real and even and, consequently has zero phase.
2. Such a filter is non-causal, since its impulse response h[n] has nonzero values for n<0.
3. However, if a causal filter is required, then a simple change in the impulse response can achieve this, resulting in a system with LINEAR phase. Specifically, since h[n] is the impulse response of an FIR filter, it is identically zero outside a range of values centered at the origin ( ie h[n] = 0 for all |n| >N).
4. If we now define the non-recursive LTI system resulting from a simple N-step delay of h[n], i.e.,
h1[n] = h[n-N]
then h1[n] =0 for all n<0, so that this LTI system is causal.
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