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From: Molly McShane on 27 Jul 2010 17:44
I'm noticing strange patterns in a bandpass butterworth filter (order 4, cutoff frequency .25/30, 2.5/30). It seems that there is a sort of sinusoidal ringing that fades to zero after about 30 sec. at both the beginning and the end of the data, where the values should be zero. The especially strange part is that the patterns are mirror copies of each other. Has anyone had this problem before or have any idea why it might be occurring and how to fix it?
Thanks!
From: Walter Roberson on 27 Jul 2010 17:46
Molly McShane wrote:
> I'm noticing strange patterns in a bandpass butterworth filter (order 4,
> cutoff frequency .25/30, 2.5/30). It seems that there is a sort of
> sinusoidal ringing that fades to zero after about 30 sec. at both the
> beginning and the end of the data, where the values should be zero. The
> especially strange part is that the patterns are mirror copies of each
> other. Has anyone had this problem before or have any idea why it might
> be occurring and how to fix it?

I am very much a novice with filters, but if I recall the Wikipedia material
on filters I was reading last week, FIR filters are inherently symmetric and
are subject to exactly the kind of ringing you refer to. There was a Good
Reason for it given there, which I do not presently remember, but might
_possibly_ have been to do with the difference between the infinite time
domain and the finite frequency domain.
From: Molly McShane on 27 Jul 2010 18:17
Do you happen to remember the name of the wikipedia article?


Walter Roberson <roberson(a)hushmail.com> wrote in message <i2nkbo$2ap$1(a)canopus.cc.umanitoba.ca>...
> Molly McShane wrote:
> > I'm noticing strange patterns in a bandpass butterworth filter (order 4,
> > cutoff frequency .25/30, 2.5/30). It seems that there is a sort of
> > sinusoidal ringing that fades to zero after about 30 sec. at both the
> > beginning and the end of the data, where the values should be zero. The
> > especially strange part is that the patterns are mirror copies of each
> > other. Has anyone had this problem before or have any idea why it might
> > be occurring and how to fix it?
>
> I am very much a novice with filters, but if I recall the Wikipedia material
> on filters I was reading last week, FIR filters are inherently symmetric and
> are subject to exactly the kind of ringing you refer to. There was a Good
> Reason for it given there, which I do not presently remember, but might
> _possibly_ have been to do with the difference between the infinite time
> domain and the finite frequency domain.
From: Walter Roberson on 2 Aug 2010 13:33
Molly McShane wrote:
> Do you happen to remember the name of the wikipedia article?
>
>
> Walter Roberson <roberson(a)hushmail.com> wrote in message
> <i2nkbo$2ap$1(a)canopus.cc.umanitoba.ca>...
>> Molly McShane wrote:
>> > I'm noticing strange patterns in a bandpass butterworth filter
>> (order 4, > cutoff frequency .25/30, 2.5/30). It seems that there is a
>> sort of > sinusoidal ringing that fades to zero after about 30 sec. at
>> both the > beginning and the end of the data, where the values should
>> be zero. The > especially strange part is that the patterns are mirror
>> copies of each > other. Has anyone had this problem before or have any
>> idea why it might > be occurring and how to fix it?
>>
>> I am very much a novice with filters, but if I recall the Wikipedia
>> material on filters I was reading last week, FIR filters are
>> inherently symmetric and are subject to exactly the kind of ringing
>> you refer to. There was a Good Reason for it given there, which I do
>> not presently remember, but might _possibly_ have been to do with the
>> difference between the infinite time domain and the finite frequency
>> domain.

I have not found the information I was thinking of, and as I am not very
familiar with filters I may have misunderstood or misremembered.

However, a FIR filter deals with discontinuous (discrete) values and so
if I understand correctly its fourier transform is inherently subject to
ringing via the Gibbs Phenomena,
http://en.wikipedia.org/wiki/Gibbs_phenomenon


With regard to symmetry,
https://ccrma.stanford.edu/~jos/filters/Symmetric_Linear_Phase_Filters.html

"As stated at the beginning of this chapter, the impulse response of
every causal, linear-phase, FIR filter is symmetric: "

I also find,
http://www.hydrogenaudio.org/forums/lofiversion/index.php/t68537.html

"According to the formula and theory,the phase response of FIR filter
whose coefficients are symmetrical is:

A(w) = -alpha*w,where alpha is a constant.

It is a strict linear single line,without discontinous points."

which appears to give a sufficient condition for linear phase (and thus
for symmetric response): that the coefficients themselves are symmetric.


I do, though, find a number of specific references to symmetric FIR
filters, which implies that non-linear phase FIR filters are not
necessarily symmetric in their response.
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