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# 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.