Frequency response (transfer function) of a two-pole bandpass filter.


Updated 17 Jul 2022

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Computes the complex frequency response function (transfer function) of a two-pole bandpass filter with specified center frequency f0 and quality factor Q.
h = filtRespTwoPoleBP(f,f0,Q)
h = filtRespTwoPoleBP(f,f0,Q) returns the frequency response column vector computed at the frequencies supplied in f (in Hz). Here f0 is the center frequency of the bandpass fiter and Q is the quality factor (sharpness, quality coefficient) of the bandpass filter. Here the definition that is used is that the –3 dB bandwidth of the bandpass filter is f0/Q.
filtRespTwoPoleBP(__) with no output arguments plots the magnitude and phase response of the specified two-pole bandpass filter (its frequency response).
filtRespTwoPoleBP() with no input arguments plots the magnitude and phase response of a number of example two-pole bandpass filters.
Note that the values of Q and/or f0 can be specified as scalars or as vectors.
If only one of these two parameters is a vector, a matrix of column vectors is returned. Each column corresponds each value given in the vector, be it Q or f0.
If both Q and f0 are vectors, e.g., Q = [2, 4] and f0 = [500, 2000], then a three-dimensional array of column vectors is returned. In this case, the second dimension corresponds to each Q(j), j=1:numel(Q), while the third dimension corresponds to each f0(k), k=1:numel(f0).
A table showing the correspondence between some Q values and filter bandwidth values in octaves is shown below.
% ---------------------
% Bandwidth Quality
% in octaves factor Q
% ---------------------
% 2 0.666667
% 1 1.414214
% 2/3 2.144908
% 1/2 2.871000
% 1/3 4.318473
% 1/6 8.651359
% ---------------------
Nello Sevastopoulos and Richard Markell. A Simple Method of Designing Multiple Order All Pole Bandpass Filters by Cascading 2nd Order Sections. Linear Technology Corporation, Application Note 27A, June 1988.

Cite As

Witold Waldman (2023). filtRespTwoPoleBP (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2022a
Compatible with any release
Platform Compatibility
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Version Published Release Notes

Updated the sample image.