Re: Why is my Butterworth filter so noisy?

[Sergei Steshenko]

--- On Mon, 9/22/08, Matthias Brennwald <address@hidden> wrote:

> From: Matthias Brennwald <address@hidden>
> Subject: Why is my Butterworth filter so noisy?
> To: address@hidden
> Date: Monday, September 22, 2008, 5:40 AM
> Dear all
> 
> I need to apply a Butterworth low-pass filter to a
> regularly sampled  
> time series of data points. I used the butter.m and
> filter.m  
> functions to do that (the butter.m function is in the
> signal package  
> from Octave-Forge). If I calculate and plot the frequency
> response of  
> the Butterworth filter using the fourier transforms of the
> original  
> and the filtered time series, the result looks like the
> expected  
> Butterworth transfer function, but with a lot of unexpected
> noise.  
> The amount of noise increases with the order of the
> Butterworth  
> filter I use.
> 
> Am I doing something wrong or am I missing something?
> 
> 
> The following is an example to reproduce the above with a
> 'faked'  
> time series:
> 
> ---------------------
> 
> N = 1000; % number of data points
> 
> t = [1:N] / N; % time
> x = 2*randn(1,N)-1; % fake time series (original data)
> 
> [b,a] = butter (6,0.3); % filter coefficients for a 6th
> order  
> Butterworth filter
> y = filter (b,a,x); % filter the original data
> 
> X = fft (x); X = X(1:N/2); % Fourier transform of the
> original data  
> (only the left part of the spectrum)
> Y = fft (y); Y = Y(1:N/2); % Fourier transform of the
> filtered data  
> (only the left part of the spectrum)
> trsf = 20*log10(abs(Y./X)); % transfer function in dB
> 
> f = [1:N/2]; % frequency
> semilogx (f,trsf) % plot the transfer function
> 
> ---------------------
> 
> 
> Matthias
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You might be interested in the following:

http://www.nabble.com/ripple-in-Butterworth-filter-created-by-'butter'-(was-"RE%3A-'long-double'-support--")-td17092962.html#a17092962
.

Regards,
  Sergei.