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.

# iirnotch

Second-order IIR notch filter

## Syntax

[num,den] = iirnotch(w0,bw)
[num,den] = iirnotch(w0,bw,ab)

## Description

[num,den] = iirnotch(w0,bw) returns the numerator coefficients, num, and the denominator coefficients, den, of the digital notching filter with the notch located at w0, and with the bandwidth at the -3 dB point set to bw. To design the filter, w0 must meet the condition 0.0 < w0 < 1.0, where 1.0 corresponds to π radians per sample in the frequency range.

The quality factor (Q factor) q for the filter is related to the filter bandwidth by q = w0/bw, where w0 is the notch frequency.

[num,den] = iirnotch(w0,bw,ab) returns the digital notching filter whose bandwidth, bw, is specified at a level of -ab decibels. Including the optional input argument ab lets you specify the magnitude response bandwidth at a level that is not the default -3 dB point, such as -6 dB or 0 dB. If not specified, ab defaults to the -3 dB width (10*log10(1/2)).

## Examples

collapse all

Design and plot an IIR notch filter that removes a 60 Hz tone (f0) from a signal at 300 Hz (fs). For this example, set the Q factor for the filter to 35 and use it to specify the filter bandwidth:

wo = 60/(300/2);  bw = wo/35;
[b,a] = iirnotch(wo,bw);
fvtool(b,a);

The notch filter has the desired bandwidth with the notch located at 60 Hz, or $0.4\pi$ radians per sample. Compare this plot to the comb filter plot shown on the reference page for iircomb.