How can I boost audio with a peak filter?

I want to boost the sound signal properly using the peak filter in Simulink. However, the peak filter has a frequency response below 0 dB. Is it appropriate to add it to the original signal? I often see peak filters with a frequency response above 0 dB as shown in the attached image. Can't this be reproduced using the notch-peak filter block in the DSP system toolbox?

[yyyo]

Answer 1

[Mathieu NOE]

hello

according to the doc

Design second-order tunable notching and peaking IIR filter - Simulink - MathWorks France

this is wha this block is doing :

IMHO this is more a passband / notch but not a audio peaking filter

the "real" audio peaking filter is given by this code below

simply export B and A arrays to a IIR simulink block and you're done !

G , gain in dB can be positive or negative as in your picture !

% demo peaking filter
%            G is the logarithmic gain (in dB)
%            FC is the center frequency
%            Q is Q-term equating to (Fb / Fc)
%            Fs is the sampling rate
fs = 44.1e3;
fc = 500;
Q = 3;
G_pos = 10; % positive dB gain 
G_neg = -20;  % negative dB gain 

[B_pos, A_pos]  = peaking(G_pos, fc, Q, fs); % put B and A in IIR simulink block
[B_neg, A_neg]  = peaking(G_neg, fc, Q, fs); % put B and A in IIR simulink block

freq = logspace(1,4,300);
[g_pos,p_pos] = dbode(B_pos,A_pos,1/fs,2*pi*freq);
[g_neg,p_neg] = dbode(B_neg,A_neg,1/fs,2*pi*freq);

figure(1)
subplot(2,1,1),semilogx(freq,20*log10(g_pos),'b',freq,20*log10(g_neg),'r');
ylabel('Gain (dB)')
subplot(2,1,2),semilogx(freq,p_pos,'b',freq,p_neg,'r');
xlabel('Freq (Hz)')
ylabel('Phase (°)')


function [B, A]  = peaking(G, fc, Q, fs)

% 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 logarithmic gain (in dB)
%            FC is the center frequency
%            Q is Q-term equating to (Fb / Fc)
%            Fs is the sampling rate
%

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];

end