MATLAB: Why wavelet doesn’t show accurate results always

frequencywaveletWavelet Toolbox

I have a signal that contains some modes in it. I've run a CWT transform but I haven't got my desired results. so I implement a test signal that contains freqs [0.1,0.3,0.6] Hz to see whats the problem with my codes. but the result was accurate. once I change the freqs to [0.1,0.4,0.6] or [0.1,0.5,0.6]Hz,The results wasn't accurate anymore on the plot. you can see the plot here, http://cubeupload.com/im/4msYBt.jpg.It might be for the damping effect of the 0.6Hz mode or … I don't know actually 🙁 I think I must fix why this happening first to get my actual signal modes. here's my codes.
t=linspace(0,30,300);
Fs=ceil(inv(t(2)-t(1)));                               % sampling freq
 x=sin(2*pi*t*0.1).*(t<10)+sin(2*pi*t*0.3).*... 
     (t<30)+sin(2*pi*t*0.6).*(t<10).*exp(-t*.1);       % my signal[0.1Hz,0.3Hz,0.6Hz] 
wname = 'morl';                                        % define wavelet name
scales = 1:1:128;                                      % scales range
coefs = cwt(x,scales,wname,'lvlabs');                  % Get coefs of x
freq = scal2frq(scales,wname,1/Fs);                    %convert scales to freq range
surf(t,freq,abs(coefs));shading('interp');             % 3D surface plot
axis tight; xlabel('Seconds'); ylabel...               % seting the axis 3D surface
    ('Pseudo-Frequency (Hz)');                         % seting the axis 3D surface

axis([0 length(t)/Fs 0 1 0 max(coefs(:))*1.1])         % seting the axis 3D surface
figure;
sc=wscalogram('image',coefs,'scales',freq,'ydata',x);  % get scalograme of x
xlabel('Time'); ylabel('Frequency of gen');            % set axis
hold on
abscof=abs(coefs)';                                    % |coefs|' 
modI=max(abscof);                                      % get  max |coefs| coresponde to freqs of x 
modI=modI/max(modI);                                   % scale each clumn 0-1
figure;
plot(freq,modI)                                        % Plot all modes. contain all 
grid on
axis([0 1 0 max(modI)*1.1])                            % seting the axis

xlabel('Pseudo-Frequency (Hz)'); ylabel('abs(coefs)'); % seting the axis

Best Answer

I'm not quite sure why you say this:
   t=linspace(0,30,300);
   Fs=ceil(inv(t(2)-t(1)));     
   x=sin(2*pi*t*0.1).*(t<10)+sin(2*pi*t*0.4).*... 
  (t<30)+sin(2*pi*t*0.6).*(t<10).*exp(-t*.1);        
   scales = 10:0.1:150;
   wname = 'morl';                                     
   coefs = cwt(x,scales,wname);                  
   freq = scal2frq(scales,wname,dt);                     
   contour(t,freq,abs(coefs));shading('interp');             
   axis tight; 
   xlabel('Time'); ylabel('Pseudo-frequency (Hz)');
You have to keep in mind that the wavelet yields a bandpass analysis.
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