# iirpeak

Second-order IIR peak or resonator filter

## Syntax

``[num,den] = iirpeak(w0,bw)``
``[num,den] = iirpeak(w0,bw,ab)``

## Description

````[num,den] = iirpeak(w0,bw)` returns a second-order digital peaking filter with the peak located at `w0`, and with the bandwidth at the `+3` dB point set to `bw`.```
````[num,den] = iirpeak(w0,bw,ab)` returns a digital peaking filter whose bandwidth, `bw`, is specified at a level of +`ab` decibels.```

## Examples

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Design and plot an IIR peaking filter that boosts the frequency at 1.75 KHz in a signal and has a bandwidth of 500 Hz at the -3 dB point.

```fs = 10000; wo = 1750/(fs/2); bw = 500/(fs/2); [b,a] = iirpeak(wo,bw); fvtool(b,a)``` The peak filter has the desired gain and bandwidth at 1.75 KHz.

## Input Arguments

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Peak frequency of the IIR filter, specified as a positive scalar in the range `(0.0,1.0)`, where 1.0 corresponds to π radians per sample in the frequency range.

Data Types: `single` | `double`

Bandwidth of the filter at a level of +`ab` decibels, specified as a positive scalar in the range `(0.0,1.0)`.

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

Data Types: `single` | `double`

Magnitude response at the filter bandwidth `bw`, specified as a scalar in dB. 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.

Data Types: `single` | `double`

## Output Arguments

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Numerator coefficients of the second order IIR peak filter transfer function, returned as a real-valued three-element row vector.

Data Types: `single` | `double`

Denominator coefficients of the second order IIR peak filter transfer function, returned as a real-valued three-element row vector.

Data Types: `single` | `double`

 S.J.Orfanidis. Introduction To Signal Processing. Englewood Cliffs, New Jersey: Prentice-Hall, 1996.

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