FIR Low Pass Filter, Phase.

Cuthbert Nyack
In most of the applets here, the phase is not shown because the behaviour is essentially the same ie a linear phase(symmetric impulse response) and constant group delay.

The Phase and Group delay as well as impulse and frequency response for a typical FIR filter is shown below for the case of a LP configuration using the Fourier series.

N is the length of the impulse response.
fc/fs is the cutoff frequency expressed as a fraction of the sampling frequency.
Frequency response is in red(linear). or green(log).
Impulse response is in pink.
Phase delay is in cyan.
and group delay in magenta.

The phase delay changes linearly with frequency and the group delay is constant. This is a consequence of the symmetric impulse response. The symmetry of the impulse response can be verified by changing nI and reading the reading the numerical value of I(nI) from the line of white text. The impulse response has a maximum value of 2 * fc/fs at nI = (N - 1)/2.

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COPYRIGHT 2008 Cuthbert A. Nyack.