Sign in
Search code
Ads
See Also
DSP Code Sharing > Peak/Notch Filter Design
Peak/Notch Filter Design
Language: Matlab
Processor: Not Relevant
Licensed under a Creative Commons Attribution 3.0 Unported License
Peak/Notch Filter Design
This function will generate the coefficients for a single IIR biquad that is a "peak/notch" design. Wierldy enough, this filter type is not part of the standard Matlab filter design toolbox. These filters are commonly used is audio signal processing to create a graphic equalizer.
For example, you may remember cassette tape players that had 5 or 10 sliders all with different frequencies to equalize the sound. Each one of those knobs represented one of these biquad types. The Center Frequency(Fc) and shape(Q) would be fixed and the knob was attached to the gain (G) parameter. If the gain is a positive dB it is said to be a peak filter and a negative dB is a notch.
See plots below to see what the magnitude response looks like:
% Derive coefficients for a peaking filter with a given amplitude and
% bandwidth. All coefficients are calculated as described in Zolzer's
% DAFX book (p. 50 - 55). This algorithm assumes a constant Q-term
% is used through the equation.
%
% Usage: [B,A] = peaking(G, Fc, Q, Fs);
%
% G is the logrithmic gain (in dB)
% FC is the center frequency
% Q is Q-term equating to (Fb / Fc)
% Fs is the sampling rate
%
% Author: sparafucile17 08/22/05
%
K = tan((pi * fc)/fs);
V0 = 10^(G/20);
%Invert gain if a cut
if(V0 < 1)
V0 = 1/V0;
end
%%%%%%%%%%%%%%
% BOOST
%%%%%%%%%%%%%%
if( G > 0 )
b0 = (1 + ((V0/Q)*K) + K^2) / (1 + ((1/Q)*K) + K^2);
b1 = (2 * (K^2 - 1)) / (1 + ((1/Q)*K) + K^2);
b2 = (1 - ((V0/Q)*K) + K^2) / (1 + ((1/Q)*K) + K^2);
a1 = b1;
a2 = (1 - ((1/Q)*K) + K^2) / (1 + ((1/Q)*K) + K^2);
%%%%%%%%%%%%%%
% CUT
%%%%%%%%%%%%%%
else
b0 = (1 + ((1/Q)*K) + K^2) / (1 + ((V0/Q)*K) + K^2);
b1 = (2 * (K^2 - 1)) / (1 + ((V0/Q)*K) + K^2);
b2 = (1 - ((1/Q)*K) + K^2) / (1 + ((V0/Q)*K) + K^2);
a1 = b1;
a2 = (1 - ((V0/Q)*K) + K^2) / (1 + ((V0/Q)*K) + K^2);
end
%return values
a = [ 1, a1, a2];
b = [ b0, b1, b2];
Comments
fresha wrote:
%%%%%%%%%%%%%%
% CUT
%%%%%%%%%%%%%%
else
b0 = (1 + ((1/Q)*K) + K^2) / (1 + ((1(V0/Q))*K) + K^2);
b1 = (2 * (K^2 - 1)) / (1 + ((1(V0/Q))*K) + K^2);
b2 = (1 - ((1/Q)*K) + K^2) / (1 + ((1(V0/Q))*K) + K^2);
a1 = b1;
a2 = (1 - ((V0/Q)*K) + K^2) / (1 + ((1(V0/Q))*K) + K^2);
fresha wrote:
ok looks like I need to find why my filter 'shifts' in a different way... :D
fresha wrote:
I stand corrected.....
and my cut divisor should have read:
(1 + ((1/(V0 * Q))*K) + K^2);
to match the book calc (doing fixed prior calcs to be more efficient opposed to calcing all the time)