Time of Flight measurement

I have a time domain signal and i want to calculate the time of flight for in general any such signals.

For that my code should detect the point of maxima(along with its time of occurence) of the first wave packet as marked in the image and the second point of maxima (along with its time of occurence). So after knowing the time of occurence of both peaks, time of flight can be calculated easily by calculating their difference.

This is easily done manually but how it can be done with the help of code?

Please help.

Answer 1

[darova]

Try this trick

p = [0.0772    0.7149
    0.1256    0.7588
    0.1878    0.8231
    0.2431    0.7646
    0.2869    0.3114
    0.3836    0.3202
    0.4597    0.3173
    0.5541    0.3348
    0.6187    0.3260
    0.6855    0.3231
    0.7339    0.4284
    0.7800    0.3845
    0.7984    0.4839
    0.8353    0.3874
    0.8813    0.3845
    0.9320    0.3465
    0.9850    0.3377];
x = p(:,1);
y = p(:,2);
plot(x,y)
[~,ix1] = max(y);               % calculate max
[~,ix2] = max(y(10:end));       % calculate max in second half of the data
ix2 = 9+ix2;
line(x(ix1),y(ix1),'marker','*')
line(x(ix2),y(ix2),'marker','*')

[Taher Sahara]

This wont work everytime as the wave packet's time may vary so everytime i have to set the range for second maximum. I want to make a generalized code which will work for all signals. The code itself must consider the range after first wave packet diminishes.

Answer 2

[Bjorn Gustavsson]

You might get somewhere by calculating the spectrogram (short-time FT) of your signal. That might allow you to identify the time for peaks of the spectral power (possibly above some cut-off-frequency?). Have a look at spectrogram.

HTH

[Bjorn Gustavsson]

Something like this:

w = 16e7; % some arbitrary f_0 in your frequency-units
t_p = 5e-6; % Pulse-length in your time-units
t = 0:(1/w):3e-4; % time
Itx = 1*sin(w*t).*double(t<t_p); % Transmitted pulse
Irx = exp(-(t)/1.4e-4).*(exp(-(t-2e-4).^2/(t_p)^2).*cos(w*t)+ exp(-(t-2.2e-4).^2/(t_p)^2).*sin(w*t)); % Received signal

subplot(3,1,1)
plot(t,Itx+Irx)                          
subplot(3,1,2)
% Calculate spectrogram:
[S,F,T,P] = spectrogram(Itx+Irx,hamming(64),16,[],(w/2/pi));
pcolor(T,F,log10(abs(S))),shading flat
caxis([-10 0]+max(caxis))
subplot(3,1,3)
%Frequency close to f_0
[df,i_fpeak] = min(abs(F-w/2/pi));                          
plot(T,log10(sum(abs(S(30:end,:)))),'.-')
hold on
plot(T,log10((abs(S(i_fpeak,:)))),'.-')  
axis([0 0.002 -10 14])

From here you should be able to extract local maxima...

[Taher Sahara]

Can i use convolute function (like envelope)?

I tried using that but i guess its not supported in 2015a version. Any alternatives?

[Bjorn Gustavsson]

Sure, you can use conv to convolve the spectral-power S, doesn't simply taking the max-value work?

[Taher Sahara]

@Bjorn Gustavsson "conv" is directly available in 2015a version? Because envelope function isnt available.

"Simply taking max value" - by this do you mean by providing the range and using max function in that range?

[Bjorn Gustavsson]

Yeah, it should be. If you cannot find conv, you can use conv2 if you just pay attention of the orientation of the inputs. If that fails you could use filtfilt (even though that would be slightly differently mathematically).

Yup. Something like this:

[Imax,idxMax] = max(S(37:end));
Tmax = T(idxMax+36);

HTH

[Taher Sahara]

Thanks for the reply, ill try conv function to create an envelope and then extract the required data.

Max function works fine when i know the range, in my case the time of arrival of wave packets may vary so every time a given range may not work. That is why im looking for an alternative.

[Bjorn Gustavsson]

But you only need to exclude the first pulse, right? The rest is signal of your interest, right? If that's the case you only need to exclude the first pulse and then the rest is where you should look for maxima. You could also simply look for local maxima, i.e. points where S(idx)-S(idx-1)>0 and S(idx+1)-S(idx)<0. You can get every such local maxima rather efficiently with diff. There might also be a file-exchange submission doing this.