How do I specify a different smoothing factor to each datapoint individually?

How do I specify a different smoothing factor to each datapoint individually? For example, for an array with 100 elements, I want the first and last 10 elements to be "fully" smoothed (smoothing factor/weight of 1), the middle elements to be unaffected (smoothing factor/weight of 0), and other elements to have a smoothing factor/weight of between 0 and 1.

[Joe Vinciguerra]

Can you post your code as you have it now, and provide your data?

Answer 1

[Mathieu NOE]

hello

that was my first idea ; coding a first order recursive filter with variable forgetting factor (or pole)

doing it forward and backward like filtfilt to avoid phase distorsion

the "window" or shape for the varaible filter is made with a inverted bell (gaussian) shape , but you can give it another shape if your prefer.

samples = 100;
x = 1:samples;
y = sin(x/10)+0.3*rand(size(x));

s = 0.75; % smoothing factor
window = (1-exp(-(x-samples/2).^2/300));

%%%%%%%%%%%%%%%%
% "smart filter" : simple first order low pass filter  
% the smoothing factor varies with time 


%% main loop 
alpha = s*window;

% forward filtering
ys = zeros(size(y));
ys(1) = y(1);

for ci = 2:samples
    % first order low pass IIR filter recursion
    ys(ci) = alpha(ci).*ys(ci-1)  + (1-alpha(ci)).*y(ci);
end

 % backward filtering
 ysflipped = ys(samples:-1:1);
 alphaflipped = alpha(samples:-1:1);
 
ys = zeros(size(y));
ys(1) = ysflipped(1);

for ci = 2:samples
    % first order low pass IIR filter recursion
    ys(ci) = alphaflipped(ci).*ys(ci-1)  + (1-alphaflipped(ci)).*ysflipped(ci);
end
 ys = ys(samples:-1:1); % flip the output

figure(1)
subplot(2,1,1)
plot(x,window);
title('Blending Factor' );
subplot(2,1,2)
plot(x,y,x,ys);legend('Raw','Smoothed');
title('Data Smoothed with home made filter' );

then I thought maybe I can achieve the same result in a shorter code , try simply to blend (with a variable factor) the raw data and a smoothed version of it

basically the two results are very similar

Now you play with the parameters of smoothdata AND the blending ratio

enjoy !

samples = 100;
x = 1:samples;
y = sin(x/10)+0.3*rand(size(x));

ys = smoothdata(y,'gaussian',15);
window = (1-exp(-(x-samples/2).^2/300));
yss = window.*ys + (1-window).*y; % blending the smoothed and non smoothed data according to window weight


figure(1)
subplot(2,1,1)
plot(x,window);
title('Blending Factor' );
subplot(2,1,2)
plot(x,y,x,yss);legend('Raw','Smoothed');
title('Data Smoothed with modified smoothdata filter' );