DTFM decoding using goertzel algorithm and peak-picking

Sorry for what will be a lengthy question. I am working on a project that will decode an array of DTMF tones. These tones can be of variable length as can the pauses between them. I am having trouble figuring out how to analyze the output of the goertzel function to distinguish between the different key strokes.

Here is what I have so far, I am sure their is a more elegant way to do it but I am just trying to get it to work before streamlining it.

First I generate the 7 DTMF frequencies using this function:

% Sinusoid.m 
% Generates a sinudoid of frequency omega_0, sampled at a frequency of 
% omega_s, for a duration of dur seconds.
function [x,t] = sinusoid(omega_0,dur,omega_s)
ts= (1)/(omega_s);
n = [0:fix(dur/ts)];
t = n.*ts;
x = sin(omega_0*t);

[x1] = sinusoid(697*pit,.25,8000*pit);
[x2] = sinusoid(770*pit,.25,8000*pit);
[x3] = sinusoid(852*pit,.25,8000*pit);
[x4] = sinusoid(941*pit,.25,8000*pit);
[y1] = sinusoid(1209*pit,.25,8000*pit);
[y2] = sinusoid(1336*pit,.25,8000*pit);
[y3] = sinusoid(1477*pit,.25,8000*pit);
[pause,t] = sinusoid(0,.25,8000*pit);

Next I sum the appropriate frequency pairs:

one = x1+y1;
two = x1+y2;
three = x1+y3;
four = x2+y1;
five = x2+y2;
six = x2+y3;
seven = x3+y1;
eight = x3+y2;
nine = x3+y3;
star = x4+y1;
zero = x4+y2;
pound = x4+y3;

Finally I create the array:

array = [eight pause eight pause eight pause four pause three pause eight pause six pause four pause three pause eight pause]; %888 438 6438

Then I run it through the my decoding function which is still a work in progress:

% phone.m 
% Takes an array of DTMF tones and decodes it into a phone number.
function [phoneNum] = phone(array)
digitIndex = find(array); % locates the non-zero indices
start = 1; % Initializing start and stop which will act at the limits of 
stop = 1;  % individual tones.
x = 1;
for k = 1:length(digitIndex)-1
    if digitIndex(k) ~= digitIndex(k+1)- 1 
        % if the values of digitIndex are non-sequential it indicates a
        % break has occured due to a pause.
        stop = k; % Sets end of array equal to break point.
        tone = array(start:start+127);
        start = digitIndex(k+2); % updates start to begining of next digit.
        TONE = goertzel(tone); % takes DFT of digit using goertzel algorithm
        subplot(4,3,x)
        stem(abs(TONE))
        title (x)
        axis([-10,210,0,100])
        x = x + 1;
    end
end

I can see that the numbers have unique characteristics so I know I am gathering the data. I just do not know how to do a peak picking algorithm that will result in the frequency pairs and allow for decoding.

I appreciate everyones time in helping out.

Answer 1

[jarick cammarato]

I figured it out. It came down to a garbage in garbage out problem. My tone generation was bad. I wound up using this code instead, it is mostly an implementation of snippets from the 'dtmfdemo' code.

symbol = {'1','2','3','4','5','6','7','8','9','*','0','#'};
lfg = [697 770 852 941]; % Low frequency group
hfg = [1209 1336 1477];  % High frequency group
f  = [];
for c=1:4,
    for r=1:3,
        f = [ f [lfg(c);hfg(r)] ];
    end
end

Fs  = 8000;       % Sampling frequency 8 kHz
N = 800;          % Tones of 100 ms
t   = (0:N-1)/Fs; % 800 samples at Fs

pit = 2*pi*t;

tones = zeros(N,size(f,2));
for button=1:12,
    tones(:,button) = sum(sin(f(:,button)*pit))';
end
one   =  tones(:,1)';
two   =  tones(:,2)';
three =  tones(:,3)';
four  =  tones(:,4)';
five  =  tones(:,5)';
six   =  tones(:,6)';
seven =  tones(:,7)';
eight =  tones(:,8)';
nine  =  tones(:,9)';
star  =  tones(:,10)';
zero  =  tones(:,11)';
pound =  tones(:,12)';
pause =  zeros(1,800);

array = [one pause two pause three pause four pause five pause six ...
    pause seven pause eight pause nine pause star pause zero pause...
    pound];

Then I defined the function Phone Decode:

% phoneDecode.m 
% Recieves an array representing variable length DTMF tones alternated with
% variable length pauses and returns a string corresponding to the phone
% number provided.
% Written by Jarick Cammarato on 11/24/12.
function [phoneNum] = phoneDecode(array)

phoneNum = [];
buttonArray =['1' '2' '3'
    '4' '5' '6'
    '7' '8' '9'
    '*' '0' '#'];
digitIndex = find(array); % locates the non-zero indices
start = 1; % Initializing start and stop which will act at the limits of 
stop = 1;  % individual tones.
x = 1;
original_f = [697; 770; 852; 941; 1209; 1336; 1477];
L = round(original_f/8000*205);  % Indices of the DFT
estim_f = round(L*8000/205);
for k = 1:length(digitIndex)-1
    if digitIndex(k) ~= digitIndex(k+1)- 1 && ...
        digitIndex(k-2) ~= digitIndex(k+1)- 4 || ...
            k == length(digitIndex) - 1  

          % if the values of digitIndex are non-sequential it indicates a
          % break has occured due to a pause. If the array end is reached
          % then the final digit must be captured.

          stop = k; % Sets end of array equal to break point.
          tone = array(start:start+204)';
          start = digitIndex(k+1); % updates start to begining of next digit.
          TONE = abs(goertzel(tone,L+1)); % takes DFT of digit using goertzel algorithm
          vert = TONE(1:4)>50;
          horz = TONE(5:7)>50;
          phoneNum = cat(2,phoneNum,buttonArray(vert,horz));
          subplot(4,3,x)
          stem(estim_f,TONE)
          title (phoneNum(:,x))
          ylabel('DFT Magnitude');
          xlabel('Frequency (Hz)')
          x = x + 1;
      end
  end
  set(gca, 'XTick', estim_f, 'XTickLabel', estim_f, 'XLim', [650 1550]);
      ylabel('DFT Magnitude');