butterworth residuals vs cutoff frequency

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joo
joo 2012-11-26
i need to apply a butterworth filter. to prove my cutoff frequency i need to do a plot ''residuals vs cutoff frequency'' like in the 2nd sqare of the picture. . residuals come from http://oi47.tinypic.com/21eokqr.jpg
so i want to apply a
-butterworth filter
-lowpass
- order n=2
- cutoff frequency wn= [0,20] hz
so my doubt is if there ia a way to find the residuals by matlab. and then plot them against cutoff frequency.
any help is huge appreciated. thank you so much
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Jan
Jan 2012-11-26
A lowpass-filter has a scalar wn frequency. For a [1 x 2] frequency a bandpass or bandstop filter is created.

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Wayne King
Wayne King 2012-11-26
编辑：Wayne King 2012-11-26
You can certainly subtract the filtered waveform from the original and plot the spectrum of that difference signal. For that you should use filtfilt() to compensate for the delay.
You do not tell us your sampling frequency, so I'll just assume 1000 for this example.
x=ecg(500)'+0.25*randn(500,1); %noisy waveform
[B,A] = butter(2,20/(1000/2));
xprime = filtfilt(B,A,x);
resid = x-xprime;
Your slide seems to suggest forming the following test statistic for various values of the cutoff frequency and examining R.
wc = [10:30]./(1000/2);
for nn = 1:length(wc)
[B,A] = butter(2,wc(nn));
xprime = filtfilt(B,A,x);
resid = x-xprime;
R(nn) = sqrt(1/length(x)*(sum(abs(x-xprime).^2)));
end
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Wayne King
Wayne King 2012-11-26
For one thing, if your sampling frequency is 40 Hz, then the cutoff frequency of 0.2 is only 4 Hz. Do you really want to limit yourself to such a low frequency here. And why start at 0? You have to keep in mind that butter() accepts normalized frequencies.
Personally, I pick the cutoff frequency based on what I know about the data and what part of the spectrum I want to focus on.
joo
joo 2012-11-26
i am sorry but i really don't understand nothing from frquencies. that 's why i want to do this plot to justificate them. i want to star at 0 to obtain a plot like http://oi47.tinypic.com/21eokqr.jpg
if you can see i posted a new quew«stion related to this http://www.mathworks.com/matlabcentral/answers/54844-butterworth-residuals-vs-cutoff-frequency-fc
thank you so much for all your help and please if you can help me with the new question i am very grateful

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