# [PD] filter phase - group delay

Charles Henry czhenry at gmail.com
Fri May 2 03:45:53 CEST 2008

```On Thu, May 1, 2008 at 9:39 AM, hard off <hard.off at gmail.com> wrote:
> from this site, in the section titled 'group delay'
>
> http://www.dspguru.com/info/terms/filtterm/index2.htm
>
>
> i got an equation to calculate the 'group delay' of a linear FIR filter.
>
> the equation is:
>
> group delay = phase shift / -2pi
>
>
> where phase shift is a value of radians / hz
>
>
> can anyone please tell me how to calculate the phase shift with a basic FIR
> filter in pd?

You can take the FFT of the FIR impulse response.  Then, phase = atan
( imag/real) where the real part != 0.

Then, just differentiate the result of atan with respect to f, and
there's your group delay.

You can make the block size arbitrarily large to get a good enough
approximation.  If you have the coefficients, and you want something
more exact... there's relevant theory in z-transforms, and probably a
better way to do the calculations.

Chuck

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```

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