"Linear Phase" refers to the condition where the phase response of the filter is a linear (straight-line) function of frequency (excluding phase wraps at +/- 180 degrees). This results in the delay through the filter being the same at all frequencies. Therefore, the filter does not cause "phase distortion" or "delay distortion". The lack of phase/delay distortion can be a critical advantage of FIR filters over IIR and analog filters in certain systems, for example, in digital data modems.
Most FIRs are linear-phase filters; when a linear-phase filter is desired, a FIR is usually used.
Most FIRs are linear-phase filters; when a linear-phase filter is desired, a FIR is usually used.
Condition for linear phase
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.)
Delay of a linear-phase FIR
Given a FIR filter which has N taps,
the
delay = (N - 1) / (2 * Fs),
where Fs is the sampling frequency.
So, for example, a 21 tap linear-phase FIR filter operating at a 1 kHz rate has delay:
(21 - 1) / (2 * 1 kHz)=10 milliseconds
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