Accelerating the pace of engineering and science

# iircomb

IIR comb notch or peak filter

## Syntax

[num,den] = iircomb(n,bw)
[num,den] = iircomb(n,bw,ab)
[num,den] = iircomb(...,'type')

## Description

[num,den] = iircomb(n,bw) returns a digital notching filter with order n and with the width of the filter notch at -3 dB set to bw, the filter bandwidth. The filter order must be a positive integer. n also defines the number of notches in the filter across the frequency range from 0 to 2π — the number of notches equals n+1.

For the notching filter, the transfer function takes the form

$H\left(z\right)=b\frac{1-{z}^{-n}}{1-\alpha {z}^{-n}}$

where α and b are the positive scalars and n is the filter order or the number of notches in the filter minus 1.

The quality factor (Q factor) q for the filter is related to the filter bandwidth by q = ω0/bw where ω0 is the frequency to remove from the signal.

[num,den] = iircomb(n,bw,ab) returns a 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.

[num,den] = iircomb(...,'type') returns a digital filter of the specified type. The input argument type can be either

• 'notch' to design an IIR notch filter. Notch filters attenuate the response at the specified frequencies. This is the default type. When you omit the type input argument, iircomb returns a notch filter.

• 'peak' to design an IIR peaking filter. Peaking filters boost the signal at the specified frequencies.

The transfer function for peaking filters is

$H\left(z\right)=b\frac{1-{z}^{-n}}{1+a{z}^{-n}}$

## Examples

Design and plot an IIR notch filter with 11 notches (equal to filter order plus 1) that removes a 60 Hz tone (f0) from a signal at 600 Hz (fs). For this example, set the Q factor for the filter to 35 and use it to specify the filter bandwidth.

```fs = 600; fo = 60;  q = 35; bw = (fo/(fs/2))/q;
[b,a] = iircomb(fs/fo,bw,'notch'); % Note type flag 'notch'
fvtool(b,a);```

Using the Filter Visualization Tool (FVTool) generates the following plot showing the filter notches. Note the notches are evenly spaced and one falls at exactly 60 Hz.