%TFDEMO1 Introduction to the Time-Frequency Toolbox.%	O. Lemoine - May 1996. %	Copyright (c) CNRS.clc; zoom on; clf; echo on;% Welcome to the Time-Frequency Toolbox for MATLAB. This demonstration % follows the plan of the tutorial, and consider exactly the same examples.% Therefore, for further information about these illustrations, we advise% you to refer to the corresponding chapter of the tutorial.  	%% Press any key to continue... pause; clc; % First let's create an analytic linear frequency modulated signal, whose % normalized frequency is changing from 0 to 0.5 :sig1=fmlin(128,0,0.5);plot(real(sig1)); axis([1 128 -1 1]);xlabel('Time'); ylabel('Real part');title('Linear frequency modulation'); grid% From this time-domain representation, it is difficult to say what kind % of modulation is contained in this signal.%% Press any key to continue...pause;% Now let's consider its energy spectrum : dsp1=fftshift(abs(fft(sig1)).^2); plot((-64:63)/128,dsp1);        xlabel('Normalized frequency'); ylabel('Squared modulus');title('Spectrum'); grid% We still can not say, from this plot, anything about the evolution in% time of the frequency content.%% In order to have a more informative description of such a signal, it % would be better to directly represent their frequency content while % still keeping the time description parameter : this is precisely the% aim of time-frequency analysis. To illustrate this, let's try the% Wigner-Ville distribution on this signal :%% press any key to continue...pause;  tfrwv(sig1);% We can see on this representation that the linear progression of the % frequency with time, from 0 to 0.5, is clearly shown.%% Press any key to continue...pause; clc; % If we now add some complex white Gaussian noise on this signal, with % a 0 dB signal to noise ratio,sig2=sigmerge(sig1,noisecg(128),0);Min=min(real(sig2)); Max=max(real(sig2)); clf; plot(real(sig2)); axis([1 128 Min Max]);xlabel('Time'); ylabel('Real part');title('Linear frequency modulation plus noise'); grid% press any key to continue...pause;% and consider the spectrum of it :dsp2=fftshift(abs(fft(sig2)).^2); plot((-64:63)/128,dsp2);        xlabel('Normalized frequency'); ylabel('Squared modulus');title('Spectrum'); grid% it is worse than before to interpret these plots. On the other hand, the% Wigner-Ville distribution still show quite clearly the linear progression% of the frequency with time : %% press any key to continue...pause;tfrwv(sig2);% press any key to continue...pause; clc; % The second example we consider is a bat sonar signal, recorded with a % sampling frequency of 230.4 kHz and an effective bandwidth equal to% [8 kHz, 80 kHz].%  First, load the signal from the MAT-file bat.mat :load batt0=linspace(0,2500/2304,2500);   clf; plot(t0,bat); xlabel('Time [ms]');axis([t0(1) t0(2500) -900 800]); grid; % From this plot, we can not say precisely what is the frequency content % at each time instant t ; similarly, if we look at its spectrum,%% press any key to continue...pause;dsp=fftshift(abs(fft(bat)).^2);f0=(-1250:1249)*230.4/2500;plot(f0,dsp); xlabel('Frequency [kHz]'); ylabel('Squared modulus');title('Spectrum'); grid% we can not say at what time the signal is located around 38 kHz, and at% what time around 40 kHz. Let us now consider a representation called % the pseudo Wigner-Ville distribution, applied on the most interesting % part of this signal (this distribution was obtained with the M-file % tfrpwv.m, stored in the matrix tfr and saved with the signal in the % MAT-file bat.m ; the corresponding time- and freqency- samples t and f % where also saved on bat.mat) :%% press any key to continue...pause;contour(t,f,tfr,5); axis('xy'); xlabel('Time [ms]'); ylabel('Frequency [kHz]'); title('TFRPWV of a bat signal'); grid% We then have a nice description of its spectral content varying with % time : it is narrow-band signal, whose frequency content is decreasing% from around 55 kHz to 38kHz, with a non-linear frequency modulation% (approximately of hyperbolic shape).%% press any key to continue...pause; clc;% The last introductory example presented here is a transient signal% embedded in a -5 dB white Gaussian noise. This transient signal is a% constant frequency modulated by a one-sided exponential amplitude :trans=amexpo1s(64).*fmconst(64);sig=[zeros(100,1) ; trans ; zeros(92,1)];sign=sigmerge(sig,noisecg(256),-5);Min=min(real(sign)); Max=max(real(sign)); subplot(211); plot(real(sign)); axis([1 256 Min Max]);xlabel('Time'); title('Noisy transient signal'); griddsp=fftshift(abs(fft(sign)).^2);subplot(212); plot((-128:127)/256,dsp); gridxlabel('Normalized frequency'); title('Energy spectrum');% From these representations, it is difficult to localize precisely the% signal in the time-domain as well as in the frequency domain.  Now let us% have a look at the spectrogram of this signal :%% press any key to continue...pause;tfrsp(sign);% the transient signal appears distinctly around the normalized frequency% 0.25, and between time points 125 and 160.%% Press any key to return to the main menu.pause;echo off