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

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2NOR_Kh 2022-7-31

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评论： Star Strider 2022-8-1

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

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Les Beckham 2022-7-31

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 2022-8-1

编辑：2NOR_Kh 2022-8-1

amghesi.mat

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.

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Answer 1

Star Strider 2022-7-31

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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.

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Star Strider 2022-8-1

在 MATLAB Online 中打开

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 2022-8-1

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 2022-8-1

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.

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