Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.

## Delay

The group delay of a filter is a measure of the average time delay of the filter as a function of frequency. It is defined as the negative first derivative of a filter's phase response. If the complex frequency response of a filter is H(e), then the group delay is

`${\tau }_{g}\left(\omega \right)=-\frac{d\theta \left(\omega \right)}{d\omega }$`

where θ(ω) is the phase, or argument of H(e). Compute group delay with

```[gd,w] = grpdelay(b,a,n) ```

which returns the `n`-point group delay, τg(ω), of the digital filter specified by `b` and `a`, evaluated at the frequencies in vector `w`.

The phase delay of a filter is the negative of phase divided by frequency:

`${\tau }_{p}\left(\omega \right)=-\frac{\theta \left(\omega \right)}{\omega }$`

To plot both the group and phase delays of a system on the same FVTool graph, type

```[z,p,k] = butter(10,200/1000); fvtool(zp2sos(z,p,k),'Analysis','grpdelay', ... 'OverlayedAnalysis','phasedelay','Legend','on')```