IIR comb notch or peak filter
For the notching filter, the transfer function takes the form:
where α and b are positive scalars and n is the filter order or the number of notches in the filter minus 1.
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 (fvt
ool) to generate the plot showing the filter notches.
Note that the notches are evenly spaced and one falls at exactly 60 Hz.
n— Order of digital filter
Order of the digital filter, specified as a positive integer.
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
bw— Bandwidth of filter
Bandwidth of the filter at a level of –
ab decibels, specified
as a positive scalar in the range
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.
ab— Magnitude response at filter bandwidth
-3(default) | scalar
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.
type— Type of digital filter
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
type input argument,
returns a notch filter.
'peak' — Design an IIR peaking filter. Peaking filters boost
the signal at the specified frequencies.
num— Numerator coefficients
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.
den— Denominator coefficients
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.
 Orfanidis, S.J., Introduction to Signal Processing, Englewood Cliffs, New Jersey: Prentice-Hall, 1996.
Usage notes and limitations:
All inputs must be constant. Expressions or variables are allowed if their values do not change.