%% 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. It is also used in systems % such as in voice mail, electronic mail and telephone banking. % % <> % Copyright 1988-2004 The MathWorks, Inc. % $Revision: 1.1.6.2 $ $Date: 2004/07/28 04:36:19 $ %% 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 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 = []; for c=1:4, for r=1:3, f = [ f [lfg(c);hfg(r)] ]; end end f' %% % 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)); 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)'); end end 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'); %% 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 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 the seven % fundamental tones. For a DFT-based solution, it has been shown that using % 205 samples in the frequency domain minimizes the error between the % original frequencies and the points at which the DFT is estimated. Nt = 205; original_f = [lfg(:);hfg(:)] % Original frequencies %% k = round(original_f/Fs*Nt); % Indices of the DFT estim_f = round(k*Fs/Nt) % Frequencies at which the DFT is estimated %% % 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 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 pad. figure, for toneChoice=1:12, % Select tone tone=tones(:,toneChoice); % Estimate DFT using Goertzel ydft(:,toneChoice) = goertzel(tone,k); % 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)'); 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. Notice that by simply % taking the component of maximum energy in the lower and upper frequency % groups, one can detect most of the symbols. Problems remain, however, % since the lowest frequency component of the upper group (1209 Hz) is % under-estimated for symbols "1", "4" and "7". To ensure proper detection, % an error control algorithm needs to be developed.