smoothing a graph using matlab

how can I smooth data imported from one column (Excel sheet) using Matlab

how to smooth the corners?

Answer 1

[Star Strider]

A frequency-selective filter can preseerve the essential shape of the signal, eliminating only the high-frequency oscillations in the ‘valleys’.

Try this —

V1 = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/900720/data.xlsx');

L = numel(V1);
t = linspace(0, L-1, L);
Ts = t(2)-t(1);
Fs = 1/Ts;
Fn = Fs/2;
NFFT = 2^nextpow2(L);
FTV1 = fft(V1,NFFT);
Fv = linspace(0, 1, NFFT/2+1)*Fn;
Iv = 1:numel(Fv);

figure
plot(Fv, abs(FTV1(Iv))*2)
grid
xlabel('Frequency')
ylabel('Amplitude')
title('Fourier Transform (Detail)')
xlim([0 0.05])

UpperPassband = 0.023;
V1F = lowpass(V1, UpperPassband, Fs, 'ImpulseResponse','iir');

figure
subplot(2,1,1)
plot(t, V1)
grid
title('Original')
subplot(2,1,2)
plot(t, V1F)
grid
xlabel('Time')
title('Filtered')

Adjust the ‘UpperPassband’ frequency to produce the desired result.

.

[Image Analyst]

This looks like it maintains the shape of the "good" part better than the Savistky-Golay filter.

[Star Strider]

I like the sgolayfilt function and use it to filter broadband noise. However, this is band-limited noise (the reason I did the fft was to determine that) so a frequency-selective filter works best in this instance.

Answer 2

[Image Analyst]

You could use sgolayfilt() to fit a sliding window to the data. Window width would be about the width of one of those humps. It looks kind of like a sine or cosine wave thus you can fit it to a 4th or 5th order polynomial. Attach your data if you need more help.

[Abeer Aboul Azm]

could you please give me an example how to do this ?

Thanks

[Image Analyst]

Attached is a generic demo I wrote. Experiment around with different parameters. If you need more help, could you attach your actual data. Otherwise could you click the "Accept this answer" link?

[Abeer Aboul Azm]

Thank you so much

Kindly could you help me to apply this on attached excel file?

[Image Analyst]

I really think you could have done it if you would have tried, but anyway, here is the simple moification I made. I read in your data (instead of creating some) with readmatrix, and I set the window width to 113 and the polynomial order to 5.

% Filter a noisy, 1-D sine wave signal using Savitzky-Golay filtering to reduce the noise.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 25;

% Read in data.
y = readmatrix('data.xlsx')
x = 1 : length(y);
% Plot the noisy signal
subplot(2,1,1);
plot(x, y, 'b-', 'LineWidth', 2);
grid on;
title('Noisy Signal', 'FontSize', fontSize);
xlabel('Index', 'FontSize', fontSize);
ylabel('Value', 'FontSize', fontSize);% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off') 

% Now smooth with a Savitzky-Golay sliding polynomial filter
windowWidth = 203-90; % Distance between a couple of peaks.
polynomialOrder = 5;
smoothY = sgolayfilt(y, polynomialOrder, windowWidth);

% Now it's done - it's smoothed.  Now plot it.
subplot(2,1,2);
plot(x, smoothY, 'b-', 'LineWidth', 2);
grid on;
caption = sprintf('Smoothed Signal with window width = %d and polynomial order = %d', windowWidth, polynomialOrder);
title(caption, 'FontSize', fontSize);
xlabel('Index', 'FontSize', fontSize);
ylabel('Value', 'FontSize', fontSize);
% Put axis in the middle
ax = gca;
ax.XAxisLocation = 'origin';

[Abeer Aboul Azm]

Thank you so much

[Image Analyst]

If it worked, can you click "Accept this answer" for the best answer? Thanks in advance.