518 What characteristic must the coefficients of an FIR filt

5.18 What characteristic must the coefficients of an FIR filter have to ensure that its frequency-domain phase response is a linear function of frequency (i.e., linear phase)?

Solution

FIR filters are usually designed to be linear-phase (but they don\'t have to be.) A FIR filter is linear-phase if (and only if) its coefficients are symmetrical around the center coefficient, that is, the first coefficient is the same as the last; the second is the same as the next-to-last, etc. (A linear-phase FIR filter having an odd number of coefficients will have a single coefficient in the center which has no mate.)