The MathWorks - Demos - Dual-Tone Multi-Frequency (DTMF) Signal Detection

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Dual-Tone Multi-Frequency (DTMF) Signal Detection

This demonstration showcases the use of the Goertzel function as a part of a DFT-based DTMF detection algorithm.

Dual-tone Multi-Frequency (DTMF) signaling is the basis for voice communications control and is widely used worldwide in modern telephony to dial numbers and configure switchboards

used in systems such as in voice mail, electronic mail and telephone banking.

ContentsGenerating DTMF Tones

Playing DTMF TonesEstimating DTMF Tones with the Goertzel AlgorithmDetecting DTMF Tones

Generating DTMF Tones

A DTMF signal consists of the sum of two sinusoids - or tones - with frequencies taken from two mutually exclusive groups. These frequencies were chosen to prevent any armonics fromincorrectly detected by the receiver as some other DTMF frequency. Each pair of tones contains one frequency of the low group (697 Hz, 770 Hz, 852 Hz, 941 Hz) and one f equency of th(1209 Hz, 1336 Hz, 1477Hz) and represents a unique symbol. The frequencies allocated to the push-buttons of the telephone pad are shown below:

1209 Hz 1336 Hz 1477 Hz_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | || | ABC | DEF |

697 Hz | 1 | 2 | 3 ||_ _ _ _ __ _ _ _ __ _ _ _ _

| | || GHI | JKL | MNO |770 Hz | 4 | 5 | 6 |

|_ _ _ _ __ _ _ _ __ _ _ _ _| | || PRS | TUV | WXY |

852 Hz | 7 | 8 | 9 ||_ _ _ _ __ _ _ _ __ _ _ _ _| | || | | |

941 Hz | * | 0 | # ||_ _ _ _ __ _ _ _ __ _ _ _ _

First, let's generate the twelve frequency pairs

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

f = [ f [lfg(c);hfg(r)] ]; end

endf'

ans =

697 1209697 1336697 1477770 1209770 1336770 1477852 1209852 1336852 1477941 1209941 1336941 1477

Next, let's generate and visualize the DTMF tones

Fs = 8000; % Sampling frequency 8 kHz

MathWorks - Demos - Dual-Tone Multi-Frequency (DTMF) Signal D... http://www.mathworks.in/products/demos/signaltlbx/dtmf/dtmfd

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N = 800; % Tones of 100 mst = (0:N-1)/Fs; % 800 samples at Fspit = 2*pi*t;

tones = zeros(N,size(f,2));for toneChoice=1:12, % Generate tone

tones(:,toneChoice) = sum(sin(f(:,toneChoice)*pit))'; % Plot tone

subplot(4,3,toneChoice),plot(t*1e3,tones(:,toneChoice));title(['Symbol "', symbol{toneChoice},'": [',num2str(f(1,toneChoice)),',',num2str(f(2,toneChoice)),']'])set(gca, 'Xlim', [0 25]);ylabel('Amplitude');

if toneChoice>9, xlabel('Time (ms)'); endendset(gcf, 'Color', [1 1 1], 'Position', [1 1 1280 1024])annotation(gcf,'textbox', 'Position',[0.38 0.96 0.45 0.026],...

'EdgeColor',[1 1 1],... 'String', '\bf Time response of each tone of the telephone pad', ... 'FitHeightToText','on');

Playing DTMF Tones

Let's play the tones of phone number 508 647 7000 for example. Notice that the "0" symbol corresponds to the 11th tone.

for i=[5 11 8 6 4 7 7 11 11 11],p = audioplayer(tones(:,i),Fs);play(p)pause(0.5)

end

Estimating DTMF Tones with the Goertzel Algorithm

The minimum duration of a DTMF signal defined by the ITU standard is 40 ms. Therefore, there are at most 0.04 x 8000 = 320 samples available for estimation and detectio . The DTMF

to estimate the frequencies contained in these short signals.

One common approach to this estimation problem is to compute the Discrete-Time Fourier Transform (DFT) samples close to the seven fundamental tones. For a DFT-based sol tion, it has


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hat using 205 samples in the frequency domain minimizes the error between the origi al frequencies and the points at which the DFT is estimated.

Nt = 205;original_f = [lfg(:);hfg(:)] % Original frequencies

original_f =

697770852941120913361477

k = round(original_f/Fs*Nt); % Indices of the DFT

estim_f = round(k*Fs/Nt) % Frequencies at which the DFT is estimated

estim_f =

702780859937121013271483

To minimize the error between the original frequencies and the points at which the DFT is estimated, we truncate the tones, keeping only 205 samples or 25.6 ms for further processing.

tones = tones(1:205,:);

At this point we could use the Fast Fourier Transform (FFT) algorithm to calculate the DFT. However, the popularity of the Goertzel algorithm in this context lies in the small number of pothe DFT is estimated. In this case, the Goertzel algorithm is more efficient than the FFT algorithm.

Plot Goertzel's DFT magnitude estimate of each tone on a grid corresponding to the telephone pad.

figure,for toneChoice=1:12, % Select tone

tone=tones(:,toneChoice); % Estimate DFT using Goertzel

ydft(:,toneChoice) = goertzel(tone,k+1); % Goertzel use 1-based indexing % Plot magnitude of the DFT

subplot(4,3,toneChoice),stem(estim_f,abs(ydft(:,toneChoice)));title(['Symbol "', symbol{toneChoice},'": [',num2str(f(1,toneChoice)),',',num2str(f(2,toneChoice)),']'])set(gca, 'XTick', estim_f, 'XTickLabel', estim_f, 'Xlim', [650 1550]);ylabel('DFT Magnitude');

if toneChoice>9, xlabel('Frequency (Hz)'); endendset(gcf, 'Color', [1 1 1], 'Position', [1 1 1280 1024])annotation(gcf,'textbox', 'Position',[0.28 0.96 0.45 0.026],... 'EdgeColor',[1 1 1],... 'String', '\bf Estimation of the frequencies contained in each tone of the telephone pad using Goertzel', ... 'FitHeightToText','on');


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Detecting DTMF Tones

The digital tone detection can be achieved by measuring the energy present at the seven frequencies estimated above. Each symbol can be separated by simply taking the component of maenergy in the lower and upper frequency groups.

Copyright 1988-2004 The MathWorks, Inc.

Published with MATLAB 7.0.4


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The MathWorks - Demos - Dual-Tone Multi-Frequency (DTMF) Signal Detection

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