Dual Tone Multi Frequency Fourier Transform

I'm trying to take Fourier Tranfrom of each tones but they are the same graph what am I missing ?

clc
clear all 
close
Fs = 8000;
N = 800;
fm = -Fs/2:Fs/N:Fs/2-1;
t = (0:N-1)/Fs;
symbols = {'1','2','3','A','4','5','6','B','7','8','9','C','*','0','#','D'};
rFreqs = [697, 770, 852, 941];                                               
cFreqs = [1209, 1336, 1477, 1633]; 
f = [];

for i = 1:4
    for j = 1:4 
       f = [ f [rFreqs(i);cFreqs(j)]];
    end
end

for toneChoice = 1:16
  tones(:,toneChoice) = sum(sin(f(:,toneChoice)*2*pi*t));
  figure(1)
  subplot(4,4,toneChoice)
  plot(t*1e3,tones(:,toneChoice)); xlim([0,25])
  title(symbols{toneChoice});xlabel("Time(ms)");ylabel("Amplitude"),
  figure(2)
  Y = abs(fft(squeeze(tones(:,toneChoice))));
  subplot(4,4,toneChoice)
  plot(Y)
  xlabel("Frequency(Hz)");ylabel("Amplitude");legend(symbols)
end

Answer 1

[Star Strider]

The Fourier transform plots are correct. I changed them to plot a one-sided transform, and this emphasizes the differences in the plotted tones. (I added an approximate frequency vector and a findpeaks call to emphgasize that the plots are correct. Eliminate them if you do not want them.)

% clc
% clear all 
% close
format shortG
Fs = 8000;
Fn = Fs/2;
N = 800;
fm = -Fs/2:Fs/N:Fs/2-1;
t = (0:N-1)/Fs;
symbols = {'1','2','3','A','4','5','6','B','7','8','9','C','*','0','#','D'};
rFreqs = [697, 770, 852, 941];                                               
cFreqs = [1209, 1336, 1477, 1633]; 
f = [];

for i = 1:4
    for j = 1:4 
       f = [ f [rFreqs(i);cFreqs(j)]];
    end
end

Fv = linspace(0,1-1/149,N/2)*Fn;                                            % Frequency Vector

for toneChoice = 1:16
  tones(:,toneChoice) = sum(sin(f(:,toneChoice)*2*pi*t));
  figure(1)
  subplot(4,4,toneChoice)
  plot(t*1e3,tones(:,toneChoice)); xlim([0,25])
  title(symbols{toneChoice});xlabel("Time(ms)");ylabel("Amplitude"),
  figure(2)
  Y = abs(fft(squeeze(tones(:,toneChoice))));
  subplot(4,4,toneChoice)
  plot(Fv,Y(1:N/2))
  grid
  xlabel("Frequency(Hz)");ylabel("Amplitude");legend(symbols(toneChoice))
  [pks,locs] = findpeaks(Y(1:N/2));                                         % Optional
  PeakFreqs = Fv(locs)                                                      % Optional
end

PeakFreqs = 1×2

1.0e+00 * 697.04 1204.9

PeakFreqs = 1×2

1.0e+00 * 697.04 1334.3

PeakFreqs = 1×2

1.0e+00 * 697.04 1473.8

PeakFreqs = 1×2

1.0e+00 * 697.04 1623.1

PeakFreqs = 1×2

1.0e+00 * 766.75 1204.9

PeakFreqs = 1×2

1.0e+00 * 766.75 1334.3

PeakFreqs = 1×2

1.0e+00 * 766.75 1473.8

PeakFreqs = 1×2

1.0e+00 * 766.75 1623.1

PeakFreqs = 1×2

1.0e+00 * 846.41 1204.9

PeakFreqs = 1×2

1.0e+00 * 846.41 1334.3

PeakFreqs = 1×2

1.0e+00 * 846.41 1473.8

PeakFreqs = 1×2

1.0e+00 * 846.41 1623.1

PeakFreqs = 1×2

1.0e+00 * 936.03 1204.9

PeakFreqs = 1×2

1.0e+00 * 936.03 1334.3

PeakFreqs = 1×2

1.0e+00 * 936.03 1473.8

PeakFreqs = 1×2

1.0e+00 * 936.03 1623.1

.