Matlab DTM Examples

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Dual-Tone Multi-Frequency (DTMF) Signal Detection

This example 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. It is also

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

Contents

Generating DTMF Tones

Playing DTMF Tones

Estimating DTMF Tones with the Goertzel Algorithm

Detecting DTMF Tones

Generating DTMF Tones

A DTMF signal consists of the sum of two sinusoids - or tones - with frequencies t aken from two mutually exclusive groups. These frequencies were chosen t o prevent any harmonics from being

incorrectly 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 frequency of the high group

(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 group

hfg = [1209 1336 1477]; % High frequency group

f = [];

forc=1:4,

forr=1:3,

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

end

end

f'

ans =

697 1209

697 1336 697 1477

770 1209 770 1336

770 1477

852 1209

852 1336

852 1477

941 1209

941 1336

941 1477

Next, let's generate and visualize the DTMF tones

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));

fortoneChoice=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');

iftoneChoice>9, xlabel('Time (ms)'); endend

set(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');

MathWorks - Examples - Dual-Tone Multi-Frequency (DTMF) Sign... http://www.mathworks.com/products/demos/signaltlbx/dtmf/dtmfdemo.html

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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.

fori=[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, t here are at most 0.04 x 8000 = 320 samples available for estimation and detection. The DTMF decoder needs

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 t he seven fundamental tones. For a DFT-based solution, it has been shown

that using 205 samples in the frequency domain minimizes the error between t he original frequencies and the points at which the DFT is estimated.

Nt = 205;

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

original_f =

697 770

852

941

1209

1336

1477

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 =

702

780

859

937

1210

1327

1483

To minimize the error be tween 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 points at which

the 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 pa d.

figure,

fortoneChoice=1:12,

% Select tone


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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');

iftoneChoice>9, xlabel('Frequency (Hz)'); end

end

set(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');

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 maximum

energy in the lower and upper frequency groups.

Copyright 1988-2004 The MathWorks, Inc.Published with MATLAB 7.0.4


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