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 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 (10log₁₀(1/2)).

Examples

Design IIR Notch Filter Using iirnotch

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);

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 for iircomb.

fvtool(b,a)

Input Arguments

w0 — Notch frequency

positive scalar

Notch frequency, specified as a positive scalar in the range 0.0 < w0 < 1.0, where 1.0 corresponds to π radiance per sample in the frequency range.

Data Types: single | double

bw — 3 dB bandwidth

positive scalar

Bandwidth at the –3 dB point, specified as a positive scalar in the range 0.0 < w0 < 1.0.

Data Types: single | double

ab — Custom decibel level

real scalar

Custom decibel level, –ab, at which the filter has a bandwidth of bw.

Data Types: single | double

Output Arguments

num — Numerator coefficients

row vector

Numerator coefficients of the designed notch filter, returned as a row vector.

Data Types: double

den — Denominator coefficients

row vector

Denominator coefficients of the designed notch filter, returned as a row vector.

Data Types: double

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.