## filtRespTwoPoleBP

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

Updated 17 Jul 2022

Computes the complex frequency response function (transfer function) of a two-pole bandpass filter with specified center frequency f0 and quality factor Q.
Syntax
h = filtRespTwoPoleBP(f,f0,Q)
filtRespTwoPoleBP(__)
filtRespTwoPoleBP()
Description
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
% ---------------------
Reference
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. https://www.analog.com/media/en/technical-documentation/application-notes/an27af.pdf

### Cite As

Witold Waldman (2023). filtRespTwoPoleBP (https://www.mathworks.com/matlabcentral/fileexchange/115125-filtresptwopolebp), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2022a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux