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iircomb

IIR comb notch or peak filter

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.

For the notching filter, the transfer function takes the form:

H(z)=b1zn1αzn

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

[num,den] = iircomb(n,bw,ab) returns a digital notching filter whose bandwidth, bw, is specified at a level of –ab decibels.

[num,den] = iircomb(___,type) returns either a digital notch filter or a digital peaking filter as specified by type.

The transfer function for peaking filters is:

H(z)=b1zn1+azn

Examples

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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'

Use the Filter Visualization Tool (fvtool) to generate the plot showing the filter notches.

fvtool(b,a);

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes object and other objects of type uitoolbar, uimenu. The axes object with title Magnitude Response (dB) contains an object of type line.

Note that the notches are evenly spaced and one falls at exactly 60 Hz.

Input Arguments

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Order of the digital filter, specified as a positive integer. n also defines the number of notches (or peaks) in the filter across the frequency range 0 to 2π. The number of notches (or peaks) equals n+1.

Data Types: single | double

Bandwidth of the filter at a level of –ab decibels, specified as a positive scalar in the range (0,1).

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.

Data Types: single | double

Magnitude response at the filter bandwidth bw, specified as a scalar in dB. You can include the optional input argument ab to specify the magnitude response at a level other than the default -3 dB, for example, -6 dB or 0 dB. If you do not include the argument ab, the function sets the magnitude response at the default -3 dB level.

Data Types: single | double

Type of the digital filter, specified as either:

  • 'notch' — 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 function returns a notch filter.

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

Output Arguments

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Numerator coefficients of the IIR filter transfer function, returned as a real-valued row vector. For an nth-order filter, the number of elements in the row vector is n+1.

Data Types: single | double

Denominator coefficients of the IIR filter transfer function, returned as a real-valued row vector. For an nth-order filter, the number of elements in the row vector is n+1.

Data Types: single | double

References

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

Extended Capabilities

Introduced in R2011a