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

Design IIR Peaking Filter

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

w0 — Peak frequency

positive scalar in the range (0.0,1.0)

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

bw — Bandwidth of filter

positive scalar in the range (0.0,1.0)

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

ab — Magnitude response at filter bandwidth

3 (default) | scalar

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

num — Numerator coefficients

real-valued three-element row vector

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

Data Types: single | double

den — Denominator coefficients

real-valued three-element row vector

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

Data Types: single | double

References

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

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

All inputs must be constant. Expressions or variables are allowed if their values do not change.