Smoothing only a part of a Curve

What functions/commands can I use to smooth only a part of my curve? Lets say I have data from x= 0 to x= 500 on the x-axis with corresponding y points. I would like to smooth only data between x= 200 to x= 400, and the rest to be the original data itself. So that sharp edges between x= 0 and x= 200 remains, and then between x= 200 to 400, I get a smooth curve part, and then beyond x= 400 it retains the original shape. There was nothing I could find that would let me smoothen only a part of my curve.

Could someone please help me on this one?

Best regards, Anirudh

Answer 1

[Image Analyst]

Just smooth everything and replace the smoothed parts, like this code:

fontSize = 25;
% Make sample signal a noisy cosine
x = 1 : 500;
period = 70;
noisySignal = 3*cos(2*pi*x/period) + rand(1, length(x));
subplot(2,2,1);
plot(x, noisySignal, 'b.-');
title('Original Noisy Signal', 'FontSize', fontSize);
grid on;
yl = ylim();
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Apply the Savitzky-Golay filter.
k = 2; % Order of the polynomial
windowSize = 25;
smoothedSignal = sgolayfilt(noisySignal, k, windowSize);
subplot(2, 2, 2);
plot(x, smoothedSignal, 'b.-');
grid on;
title('Savitzky-Golay Filtered Signal', 'FontSize', fontSize);
% Make y limits be the same.
ylim(yl);

% Make a new signal with x=200 to 400 being smooth
newSignal = noisySignal; % Initialize.
newSignal(200:400) = smoothedSignal(200:400);
subplot(2, 2, 3:4);
plot(x, newSignal, 'b.-');
grid on;
title('Composite Signal', 'FontSize', fontSize);
% Make y limits be the same.
ylim(yl);

You might also be interested in this from the Mathworks: http://www.mathworks.com/matlabcentral/answers/103916-how-can-i-smooth-a-signal-while-preserving-peaks-in-matlab-r2013a

[Anirudh]

Hello,

Thank you so much for the response. I could use the part of the code. However I have a small problem. It could be that I could have explained my problem in detail.

Here it goes, my y-coordinates corresponds to a trace as in the link. http://articles.sae.org/5673/ Assume there is a triangular sharp peak instead of a curved one to this image. Now how do I smoothen only the part from x=720 to x=820 with different smoothing windows?

The second part of my question would be when I join a smoothed curve with an original measurement data, I would want the point of joining to have minimum or no error, would that be possible?

Looking forward to your response.

Regards, Anirudh

[Image Analyst]

It's virtually the same code. I don't really care WHERE you get noisy signal - I just made up the cosine curve because I needed some data. Of course you can get it however you need to , such as reading it in from a file, or whatever. After that the code is the same. Basically, filter it all and replace the chunk you want to with the filtered data.

[Anirudh]

Hi,

Its me again. And I'm still not satisfied with the curves I have :(. The specificity of my problem now lies in the convergence of both raw and smooth signals.

I'm attaching a file for your reference with the raw signals. This is exactly what I have, and I only need to smooth-en the peak which is around the x=800 mark with a smoothing window that could decide how much to do so.

While the constant slope from around x=720 to the point where smoothing of the peak starts needs to be from the original raw data. So in effect, I need the raw data up until the start of the peak, then the smoothed part, and then back with the original data once the smoothed signal rejoins the original signals. Could that be done?

Looking to hear your views Image Analyst, thanks a ton for your time.

Regards, Anirudh