, where is the length impulse
response of a causalFIR filter. Causal recursive filters cannot have
symmetric impulse responses.
We will show that every symmetric impulse response corresponds to a
realfrequency response times a
linear phase term
is the slope of the linear phase. Linear phase is
often ideal because a filter phase of the form
corresponds to phase delay
That is, both the phase and group delay of a linear-phase filter are
equal to samples of plain delay at every frequency.
Since a length FIR filter implements samples of delay, the
value is exactly half the total filter delay. Delaying
all frequency components by the same amount preserves
the waveshape as much as possible for a given amplitude response.