iirpeak.m

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%> @file iirpeak.m
function [num, den] = iirpeak(Wo, BW, varargin)
%IIRPEAK Second-order IIR peaking (resonator) digital filter design.
%   [NUM, DEN] = IIRPEAK(Wo, BW) designs a second-order resonator digital
%   filter with the peak at frequency Wo and a bandwidth of BW at the 3 dB
%   level. Wo must satisfy 0.0 < Wo < 1.0, with 1.0 corresponding to pi
%   radians/sample.
%
%   The bandwidth BW is related to the Q-factor of a filter by BW = Wo/Q.
%
%   [NUM, DEN] = IIRPEAK(Wo, BW, Ab) designs a peaking filter with a bandwidth
%   of BW at a level Ab in decibels. If not specified, Ab defaults to the
%   3 dB width (10*log10(2)).
%
%   EXAMPLE:
%      % Design a filter operating at a rate of 10 kHz that has a peak at
%      % 1.75 kHz and a 3 dB width of 500 Hz.
%      Fs = 10000; Wo = 1750/(Fs/2);  BW = 500/(Fs/2);
%      [b, a] = iirpeak(Wo, BW);
%      fvtool(b, a);
%
%   See also IIRNOTCH, IIRCOMB, FIRGR.
% 
%   Author(s): P. Pacheco
%   Copyright 1999-2006 The MathWorks, Inc.
%   $Revision: 1.1.4.4 $  $Date: 2007/12/14 14:34:01 $
% 
%   References:
%     [1] Sophocles J. Orfanidis, Introduction To Signal Processing
%         Prentice-Hall 1996.
 
narginchk(2, 3);
 
% Validate input arguments.
[Ab, msg] = notchpeakargchk(Wo, BW, varargin);
if ~isempty(msg)
    error(generatemsgid('FilterErr'), msg);
end
 
% Design a peaking filter.
[num, den] = secondorderPeak(Wo, BW, Ab);
 
 
 
function [num, den] = secondorderPeak(Wo, BW, Ab)
% Design a 2nd order IIR peaking (resonator) digital filter.
 
% Inputs are normalized by pi.
BW = BW*pi;
Wo = Wo*pi;
 
Gb   = 10^(-Ab/20);
beta = (Gb/sqrt(1-Gb.^2))*tan(BW/2);
gain = 1/(1+beta);
 
num  = (1-gain)*[1 0 -1];
den  = [1 -2*gain*cos(Wo) (2*gain-1)];
 
 
% [EOF]