filtRespTwoPoleBP

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

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