Comparison of waveforms with Savitzky-Golay filter

Hi,

I have managed to produce the plot of different filters on the same noisy signal. I would like to be able to compare each smoothed signal with the noisy signal. However I think the way I am running the codes I am over writing the previous smoothing filter and just plotting the results. Will this affect the comparison when I choose to compare the noisy signal with any of the filters?

This is how I currently run the codes:

load 'SineNoise'

Filter1

Filter2

Filter3

Filter4

Filter5

Plot

1) load 'SineNoise'

- This is the same from previous post

2) Filter1

N = 2; % Order of polynomial fit 2,4,6,8

F = 11; % Window length 11,23,35,47,59

[b,g] = sgolay(N,F); % Calculate S-G coefficients

HalfWin = ((F+1)/2) -1;

for n = (F+1)/2:(length(x)-5)-(F+1)/2,

% Zeroth derivative (smoothing only) SG0(n) = dot(g(:,1),y(n - HalfWin:n + HalfWin)); end

%Plot against x 0,0.1,0.2,....,

plot(x(1:length(SG0)),y(1:length(SG0)));

hold on

plot(x(1:length(SG0)),SG0','y','LineWidth',2.5);

3) Filter2 to Filter5 are pretty much the same except for the F value changing.

N = 2; % Order of polynomial fit 2,4,6,8

F = 23; % Window length 11,23,35,47,59

[b,g] = sgolay(N,F); % Calculate S-G coefficients

HalfWin = ((F+1)/2) -1;

for n = (F+1)/2:(length(x)-5)-(F+1)/2,

% Zeroth derivative (smoothing only) SG0(n) = dot(g(:,1),y(n - HalfWin:n + HalfWin)); end

%Plot against x 0,0.1,0.2,....,

plot(x(1:length(SG0)),SG0','m','LineWidth',2.5);

4) Plot - changing the axis and background colour aswell as legend

axis ([480 520 -20 20]); %changes view of axis to certain limits

legend('Noisy data','Filter1', 'Filter2', 'Filter3', 'Filter4', 'Filter5')

set(gca,'Color',[0.8 0.8 0.8]); %changes background colour to grey

ylabel('Noisy Signal')

I am just curious if it's possible when comparing the filter with the noisy signal to do something like this: Difference between the filter and the noise for each data point at a certain range (say from 480-520) and the average between the two. I am basically just looking for a number or a percentage difference between the two waveforms.

Or is there another/better way to compare the waveforms?

Thanks

Answer 1

[Image Analyst]

There are several ways, such as RMS, mean absolute difference, PSNR, etc. Sounds like you're mostly describing the mean absolute difference. I suppose it's as good a way as any. It should work for your purposes, I would guess.

[Vince Roman]

How could I apply it within the codes shown above. I use it after I apply a filter at a time?