For a discrete-time filter to be causal and to have exactly linear phase, its impulse re...

For a discrete-time filter to be causal and to have exactly linear phase, its impulse response must be of finite length and consequently the difference equation must be nonrecursive. To focus on the insight behind this statement, we consider a particular case, that of a linear phase characteristic for which the slope of the phase is an integer. Thus, the frequency response is assumed to be of the form