# How can I smooth this plot?

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Lala0099 13 Nov 2019
Commented: Star Strider 15 Nov 2019
So i have a large data set. I just copied here one set, as an example. I tried to use filters to get rid of those small spikes, but i ended up with just a completely straight line.
I split this data in thre sectoins (720 length each) , because I want to kee that stepping characteristic of it.
I am using R2017b edition of matlab, so there are many functions i cannot use to do this.
Could anyone help me with this?

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Star Strider 13 Nov 2019
Try this:
signal = D(:,1);
L = size(signal,1);
Fs = 1; % Sampling Frequency (Default, Time Vector Or Sampling Frequency Not Provided)
Fn = Fs/2; % Nyquist Frequency
msig = signal - mean(signal);
FTsig = fft(msig)/L; % Subtract Mean (Makes FFT Easier To Interpret)
Fv = linspace(0, 1, fix(L/2)+1)*Fn; % Frequency Vector
Iv = 1:numel(Fv); % Index Vector
figure
plot(Fv, abs(FTsig(Iv))*2)
grid
xlim([0 0.05])
% Fs = 2250; % Sampling Frequency
% Fn = Fs/2; % Nyquist Frequency
Wp = 0.019*Fs/Fn; % Stopband Frequency (Normalised)
Ws = 1.2*Wp; % Passband Frequency (Normalised)
Rp = 1; % Passband Ripple
Rs = 60; % Passband Ripple (Attenuation)
[n,Wp] = ellipord(Wp,Ws,Rp,Rs); % Elliptic Order Calculation
[z,p,k] = ellip(n,Rp,Rs,Wp,'low'); % Elliptic Filter Design: Zero-Pole-Gain
[sos,g] = zp2sos(z,p,k); % Second-Order Section For Stability
figure
freqz(sos, 2^18, Fs) % Filter Bode Plot
set(subplot(2,1,1), 'XLim',[0 Fs/5]) % Optional
set(subplot(2,1,2), 'XLim',[0 Fs/5]) % Optional
signal_filt = filtfilt(sos, g, signal); % Filter Signal
t = linspace(0, 1, L)/Fs; % Time Vector
figure
plot(t, signal, '-b')
hold on
plot(t, signal_filt, '-r', 'LineWidth',1.5)
hold off
grid
xlabel('Frequency')
ylabel('Amplitude')
legend('Original Signal', 'Filtered Signal', 'Location','SW')
It designs a lowpass filter that filters out most of the noise:
The stopband ‘Ws’ is set to be a specific multiplier of the passband frequency, so you only need to change ‘Wp’ to get different passband and stopband frequencies.
Experiment to get the result you want.

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Star Strider 14 Nov 2019
Lala0099 15 Nov 2019
I did more background reading on elliptic filters and now it makes sense! Thank you !
Star Strider 15 Nov 2019
As always, my pleasure!

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Henry Gotjen 13 Nov 2019
A little more crudely than Strider's answer, since you may not have some of those functions in R2017...
Here is a function that cuts a function up at significant discontinuites and smooths the individual parts. If you don't have the smooth function, replace it with a simple one from the file exchange like https://www.mathworks.com/matlabcentral/fileexchange/19998-fast-smoothing-function
function xs = smoothsmallstuff(x,w)
sig = 6;
x = x(:);
dx = diff(x);
mdx = mean(dx);
sdx = std(dx);
idiscont = [1; find(abs(dx-mdx)/sdx>6); length(x)];
xs = x;
for i = 1:length(idiscont)-1
sect = idiscont(i):idiscont(i+1);
xs(sect) = smooth(x(sect),w);
end
end

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Lala0099 14 Nov 2019
I tried the smooth function before but it did not work. If i dont have those step like decreases in my output, just a simple signal with spikes, then how could I smooth the signal ?
Henry Gotjen 14 Nov 2019
Did you include the, smoothing width when you used the function?
smooth(x,width) % width = index-width of moving average. Default is 5 points
The default smoothing width is only 5 points. Since your data is really large >1000 points, 5pt smoothing appear effective. Try:
smooth(x,300)
Note this will also smooth out larg discontinuities, hence the function i wrote above.

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