butterworth residuals vs cutoff frequency

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

[Jan]

A lowpass-filter has a scalar wn frequency. For a [1 x 2] frequency a bandpass or bandstop filter is created.

Answer 1

[Wayne King]

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

[joo]

OHH thankkkkk you so much. i am doing this plot to determine my cutoff freq.my sample freq is 40 hz.the result seems very good but the first part of the plot is strange. do you see where is the mistake? http://i46.tinypic.com/250kzk7.jpg. i use this data <http://www.speedyshare.com/b6ZCH/qq.xlsx >> and this code

fileName = 'qq.xlsx';

      excel = xlsread(fileName);
      x = excel(:,1);
           wc =0:0.0001:0.2
           for nn= 2:length(wc)
              [B,A] = butter(2,wc(nn));
              xprime = filtfilt(B,A,x);
              R(nn) = sqrt(1/length(x)*(sum((x-xprime).^2)));
           end
              plot(wc*100,R, '*')

thank you so much for all your kindness

[joo]

also, is there a way to know the cutoff directly in matlab, without doing this plot? thank you

[Wayne King]

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]

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