While the trivial ``bypass filter'' was zero-phase, the ``bypass filter with a unit delay,'' is linear phase. We know this because it is (trivially) symmetric about time . Since the frequency response is , the phase- and group-delays are each 1 sample at every frequency.
The impulse response of the simplest lowpass filter studied in
Chapter 1 was
(or in matlab syntax,
h=[1 1]). Since this impulse response is symmetric about time
samples, it is linear phase, and
as derived in Chapter 1.
The phase delay and group delay are both sample at