Q2Digital Signal Processing
Question
2 marks
Q.2. What conditions are to be satisfied by the impulse response of an FIR system in order to have a linear phase?
Answer
For linear phase, the FIR impulse response must be symmetric (h(n) = h(M-1-n)) or antisymmetric (h(n) = -h(M-1-n)) about its center.
An FIR filter with impulse response h(n), 0 ≤ n ≤ M-1, has exactly linear phase if and only if h(n) exhibits symmetry (h(n) = h(M-1-n), giving a constant group delay with zero phase distortion within the passband) or antisymmetry (h(n) = -h(M-1-n), giving linear phase with a constant 90° phase shift, useful for differentiators and Hilbert transformers) about the center point n = (M-1)/2 of the sequence.