Re: Why is my Butterworth filter so noisy?

[Julius Smith]

Another option is to design the Butterworth zeros and poles and then
call zp2sos() to convert to (real) series second-order sections.

The "noise" in the original post is due to missing frequencies in the
input signal, resulting in spurious numerical failures in the spectral
ratio Y./X.  If you replace the line

x = 2*randn(1,N)-1; % fake time series (original data)

by

x = [1,zeros(1,N-1)]; % impulse

then the response looks fine.  To use noise as an input, it is
necessary to do a lot more averaging over time (see the topic of
system identification, for example).

- jos

On Mon, Sep 22, 2008 at 11:38 AM, Sergei Steshenko <address@hidden> wrote:
>
>
>
> --- On Mon, 9/22/08, Matthias Brennwald <address@hidden> wrote:
>
>> From: Matthias Brennwald <address@hidden>
>> Subject: Re: Why is my Butterworth filter so noisy?
>> To: address@hidden, address@hidden
>> Date: Monday, September 22, 2008, 10:27 AM
>> On 22.09.2008, at 18:12, Sergei Steshenko wrote:
>>
>> > 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
>>
>> Ok. So THE recommended way of using butter.m is to not
>> return the
>> filter coefficients, but the have it return the poles,
>> zeros, and the
>> gain. So I'd to the following:
>>
>> [z,p,g] = butter (...)
>>
>> Now, how should I use z, p and g to filter my data? I
>> believe I
>> cannot use filter.m with these data.
>>
>> Matthias
>
> There is an example script below the message, it shows how to use poles and
> zeros. I mean the
>
> http://www.nabble.com/ripple-in-Butterworth-filter-created-by-'butter'-(was-"RE%3A-'long-double'-support--")-td17092962.html#a17092962
> .
>
> Look for
>
> # good accuracy BEGIN
>
> and for znom (i.e. nominator in z-plane, zeros) and zdenom (denominator
> in z-plane, poles) and a couple of 'for' loops - everything is very
> straightforward.
>
> Regards,
>  Sergei.
>
>
>
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