I am designing a notch filter that removes unwanted frequencies at 60, 120 and 180 Hz for a VoIP call sampled at 180000 kHz. Here is my filter implemented in Scilab.

clc; clear; close;

fs = 16000;
F  = [60, 120, 180];
BW = 3;
Nsec = length(F);

bmat  = zeros(Nsec,3);
amat  = zeros(Nsec,3);
rvec  = zeros(1,Nsec);
w0vec = zeros(1,Nsec);

for k = 1:Nsec
    f0 = F(k);
    w0 = 2*%pi*f0/fs;
    r  = exp(-%pi * BW / fs);
    b  = [1, -2*cos(w0), 1];
    a  = [1, -2*r*cos(w0), r^2];
    bmat(k,:) = b;
    amat(k,:) = a;
    rvec(k)   = r;
    w0vec(k)  = w0;
end

mprintf("Frecuencias: %s Hz\n\n", string(F));
for k = 1:Nsec
    mprintf("Seccion %d: f0=%3d Hz\n", k, F(k));
    mprintf(" b (float) = [ %.10f, %.10f, %.10f ]\n", bmat(k,1), bmat(k,2), bmat(k,3));
    mprintf(" a (float) = [ %.10f, %.10f, %.10f ]\n\n", amat(k,1), amat(k,2), amat(k,3));
end

z = %z;
Hz_all = 1;
for k = 1:Nsec
    w0 = w0vec(k);
    z1 = exp(%i*w0);
    z2 = exp(-%i*w0);
    p1 = rvec(k)*exp(%i*w0);
    p2 = rvec(k)*exp(-%i*w0);
    num1 = real((z - z1)*(z - z2));
    den1 = real((z - p1)*(z - p2));
    Hk = num1 ./ den1;
    Hz_all = Hz_all .* Hk;
end

[h1, fr] = frmag(Hz_all, 2048);
freqHz = fr * fs;
magdB = 20*log10(h1);

figure;
plot2d(freqHz, magdB);
xtitle("Magnitude response (all notches cascaded)", "Frequency (Hz)", "Magnitude (dB)");
xgrid();

figure;
for k = 1:Nsec
    w0 = w0vec(k);
    z1 = exp(%i*w0);
    z2 = exp(-%i*w0);
    p1 = rvec(k)*exp(%i*w0);
    p2 = rvec(k)*exp(-%i*w0);
    Hk = real((z - z1).*(z - z2)) ./ real((z - p1).*(z - p2));
    [hk, frk] = frmag(Hk, 1024);
    subplot(Nsec,1,k);
    plot2d(frk*fs, 20*log10(hk));
    xtitle("Seccion "+string(k)+" Magnitude (dB)", "Freq (Hz)", "dB");
    xgrid();
end

and the floating-point coefficients I obtained.

Frecuencies: 60 Hz

Section 1: f0= 60 Hz
 b (float) = [ 1.0000000000, -1.9994448604, 1.0000000000 ]
 a (float) = [ 1.0000000000, -1.9982674370, 0.9988225964 ]

Section 2: f0=120 Hz
 b (float) = [ 1.0000000000, -1.9977797499, 1.0000000000 ]
 a (float) = [ 1.0000000000, -1.9966033070, 0.9988225964 ]

Section 3: f0=180 Hz
 b (float) = [ 1.0000000000, -1.9950055928, 1.0000000000 ]
 a (float) = [ 1.0000000000, -1.9938307836, 0.9988225964 ]

For testing, I want to generate a simple multitone test noise and visualize it with an FFT. Since I am still a student, I would like to know what characteristics the multitone noise should have to realistically simulate a VoIP call, and which practical aspects I should consider when generating that test noise.

 

Why are you sampling a VoIP call at 180 MHz?

 

White noise. The comb filters should then show minimums at those frequencies with all others at the same magnitude.

 

Why are you sampling a VoIP call at 180 MHz?

I'm getting the coefficients for every notch with respect to sampling frecuency. I've been told that greater frecuencies higher than those I specified can cause degradation of audio quality.

 

I'm getting the coefficients for every notch with respect to sampling frecuency. I've been told that greater frecuencies higher than those I specified can cause degradation of audio quality.

I'm asking why you are sampling at 180 MHz. Typical VoIP sampling rates are typically 8 kHz (i.e., 0.008 MHz), though some codecs go as high as 48 kHz. You are sampling more that twenty-two thousand times faster than most codecs. Why?

 

I'm asking why you are sampling at 180 MHz. Typical VoIP sampling rates are typically 8 kHz (i.e., 0.008 MHz), though some codecs go as high as 48 kHz. You are sampling more that twenty-two thousand times faster than most codecs. Why?

Well in the specifications, I've been said that sampling frecuency for VoIP call are 16000 Khz, but I didnt know that I was sampling 180 Mz. It's just I dont know the notations in scilab. O'm Sorry. In which part of the code is the sampling of 180 MHz ?

 

Well in the specifications, I've been said that sampling frecuency for VoIP call are 16 Khz, but I didnt know that I was sampling 180 Mz. It's just I dont know the notations in scilab. O'm Sorry, I mistake in the formulation of the problem. But I'd like to know the feature of the noise.

 

First, in post #1, it was:

180000 kHz.

Next, in post #6 it was:

16000 Khz

Now, in post #7, it is

16 Khz