how to fit an exponential curve to my signal in a plot?

I have a signal and I should fit an exponential curve to it. This curve should be made based on the max imum peaks in the signal. To make it more clear I attached a photo of what I am looking for.

I appreciate any help

[Les Beckham]

That signal doesn't look even remotely like an exponential. You need to provide more information about what your goal is. For example, why do you need to do such a curve fit.

Also, it is always easier to get help if you provide your data and whatever code you have done so far to try to achieve your goals. Then we can provide specific help with specific issues.

Currently, this question is much too vague.

[2NOR_Kh]

it's a line of ultrasound in the liver. Based on the physics of ultrasound, the sound will attenuate as a function of time or depth. This attenuation is an exponential term, a decay exponential term. The simplest way to estimate attenuation is to find an exponential curve that will fit the peaks of the signal. I know there is a bunch of fit distribution functions in MATLAB but I couldn't find anything which will fit a curve based on the peaks in the diagram.

I upploaded my signal.

Answer 1

[Star Strider]

It would help to have the signal. There appears to be high-frequency noise, so the first step would be to calculate the one-sided fft, amd then using that information, design a lowpass or bandpass filter to filter it out, using the 'ImpulseResponse','iir' name-value pair for best results. The envelope function would then be helpful in defining the exponential characteristic.

I doubt that without some pre-processing it would be possible to define an exponential envelope for those data.

[2NOR_Kh]

Thank you Star for your comment. I eddited my signal and now have the envelope as you said. I upploaded my file.

[Star Strider]

I am sorry to discourage you, however wanting to get anything out of the signal you atached is essentially wishful thinking. That signal does not have any sort of exponential envelope, and no amount of filtering to eliminate the noise (of which there is much) will recover anything of value from it.

I tried a bandpass, lowpass, and Savitzky-Golay (sgolayfilt that is best for broadband noise, with varying ‘framelen’ values) filters on it, and had poor results for all of them.

LD = load('amghesi.mat');
m3h = LD.m3h;
Fs = 1;                                                                     % Sampling Frequency Needs To Be Stated Specifically
Fn = Fs/2;                                                                  % Nyquist Frequency
L = numel(m3h);
t = linspace(0, L-1, L)/Fs;                                                 % Time Vector

NFFT = 2^nextpow2(L);
FTm3h = fft(m3h-mean(m3h),NFFT)/L;                                          % Subtract The Mean To Make Other Peaks More Easily Visible
Fv = linspace(0, 1, NFFT/2+1)*Fn;
Iv = 1:numel(Fv);

figure
plot(Fv, abs(FTm3h(Iv))*2)
grid
xlabel('Frequency')
yalbel('Amplitude')

% m3hf = lowpass(m3h,0.15*Fs, Fs, 'ImpulseResponse','iir');
% m3hf = bandpass(m3h,[0.005 0.15]*Fs, Fs, 'ImpulseResponse','iir');
m3hf = sgolayfilt(m3h, 3, 71);

figure
plot(t, m3hf)
grid

There is just nothing in that signal that in any way suggests an exponential envelope, no matter what filters aare used.

.

[2NOR_Kh]

Star,

thank you so much, your help means a lot for me.

I really appreciate your time and help.

I hope you the best things!

after hours of reading papers, I realized that this attenuation coefficient (a) that I am looking for(exp(-a*f)). is a function of frequency and depth. but this signal that I was working on and uppload here, is amplituded based on depth. So, I think I should apply fft in small regions and then shiftting, so at the end I'll have fft of each region and this can be interpreted as frequency and depth information and an exponential curve could be fitted to that.

finger crossed to find that coefficient ;-)

[Star Strider]

My pleasure!

If you want to plot frequency as a function of time and depth, the pspectrum function with the 'spectrogram' option would likely be best. I have no idea what your other data look like, so I cannot be certain, however that would be what I would do next.

[2NOR_Kh]

I'll start fixing it today. Even I myself don't have any idea how this should look like but this exponential curve is comming from the physics of ultrasound and it should work.

[Star Strider]

I am not certain what your data are, so I cannot suggest any other approaches. The one file that was supplied was significantly different from the plot image in the original post. I have no idea how — or if — they are related.

If you have not already searched the literature, the best option would be to do a PubMed search to see how others have approached this problem. Ultrasound has been available for about a half century, so there is likely literature on the problem you are working with that could make the analysis easier.