How to get magnitude values for a Parametric EQ?

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I was doing pretty well with analog filters, but I can't seem to get similar results with digital filters.
Here's what I tried first. Link to my xlsx data.
%% load stuff
M = readtable('dB Technologies T4 PS1.xlsx','Sheet','TF');
%% create filter
Fs = 96e3;
N1 = 2;
G = -5; % 5 dB
Wo = 100/(Fs/2);
BW = 4000/(Fs/2); % Need to figure out how to insert BW in octaves.
[b,a] = designParamEQ(N1,G,Wo,BW);
%% calculate magnitude response
w = M.Frequency_Hz;
h = freqz(b,a,w);
magdB = mag2db(abs(h));
That didn't work, so I tried create a biquad filter from the parametric filter.
BQ = dsp.BiquadFilter('SOSMatrix',[b.',[1,a.']]);
h = freqz(BQ);
That didn't work either. I thought maybe it had something to do with my frequency needing to be converted to radians per sample...
wRad = w*((2*pi)/(Fs/2));
But that didn't work either. What am I missing here?
By the way, I was able to visualize the BQ filter with fvtool, so I could see it was working. I just have been able to get a magnitude response form it.

Accepted Answer

Brian Hemmat
Brian Hemmat on 22 Aug 2020
Edited: Brian Hemmat on 27 Aug 2020
Hi Nathan,
The syntax of freqz that you were using in your code above expects w to be normalized fequency. I ran your code and its not normalized. You can specify frequency in Hz by also specifying the sample rate.
Another issue (updated answer): is that the default orientation of the coefficients output from designParamEQ was not the orientation expected by fvtool and freqz.
M = readtable('spec.xlsx','Sheet','TF');
Fs = 96e3;
N = 2;
G = -5; % 5 dB
Wo = 1000/(Fs/2); % center frequency
BW = 1; %bandwidth in octaves
Q = sqrt(2^BW)/((2^BW)-1); % convert bandwidth to Q
BWnorm = Wo/Q; % then to normalized bandwidth
[b,a] = designParamEQ(N1,G,Wo,BWnorm,'Orientation','row');
% Magnitude and phase of parametric EQ
f = M.Frequency_Hz;
h = freqz([b,a],f,Fs);
magdB = mag2db(abs(h));
% plot
semilogx(f,magdB) % the filter
grid on
% ylim([-24 24]);
% xlim([20 20000]);
legend('Mag Parametric EQ','Location','best');
Nathan Lively
Nathan Lively on 28 Aug 2020
We did it! Well, you did it. :)
Brian, thank you so much. It's been a struggle for me to get started because I know a little about being a sound engineer, but almost nothing about math or programming.
Here's the result.
Would you be willing to take a stab at helping figure out the same problem, but with an allpass filter?

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