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Isaac Gerg
Guest
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 Posted:
Thu Dec 16, 2004 9:25 pm Post subject:
Bandpass filter techniques |
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Some bandpass filters I have heard of:
1. Chebyshev
2. Butterworth
3. Raised Cosine
What are the attribtues of theses filters that make ones more useful
than another in a given sitation?
Iasac |
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Wolfgang
Guest
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| Posted:
Thu Dec 16, 2004 10:39 pm Post subject:
Re: Bandpass filter techniques |
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The shape of the filter curve.
(e.g. some have a ripple in stop-band, some a ripple in pass-band, some have
no ripple but poorer cross over from pass band to stop band)
Regards, Wolfgang |
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Jerry Avins
Guest
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| Posted:
Thu Dec 16, 2004 10:41 pm Post subject:
Re: Bandpass filter techniques |
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Isaac Gerg wrote:
| Quote: | Some bandpass filters I have heard of:
1. Chebyshev
2. Butterworth
3. Raised Cosine
What are the attribtues of theses filters that make ones more useful
than another in a given sitation?
Iasac
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Google will turn up lots of information.
What is your background? How much math are you comfortable with? What is
the context that you are looking into?
A few more types:
Linear phase
Bessel (or Cauer)
Linkwitz-Riley
Chebychev Type II
Most bandpass and highpass filters are derived from lowpass prototypes.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Isaac Gerg
Guest
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| Posted:
Thu Dec 16, 2004 11:26 pm Post subject:
Re: Bandpass filter techniques |
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I am very comfortable with the mathematics behind filtering. I am just
looking for a high level view of the 3 filters I listed. It has been
some time since I have done 1D signal filtering and just inquiring as to
why one would want to use oen filter over another (e.g. Why doesnt
everyone just use a raised cosine filter).
I am very familier with image processing techniques in which mostly
Butterworth and Gaussian bandpass filters are used. However, it seems
that 1D dsp is more concentrated on different filter types than in 2d dsp.
Any enlightenment please.
Isaac |
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Jerry Avins
Guest
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| Posted:
Fri Dec 17, 2004 12:46 am Post subject:
Re: Bandpass filter techniques |
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Isaac Gerg wrote:
| Quote: | I am very comfortable with the mathematics behind filtering. I am just
looking for a high level view of the 3 filters I listed. It has been
some time since I have done 1D signal filtering and just inquiring as to
why one would want to use oen filter over another (e.g. Why doesnt
everyone just use a raised cosine filter).
I am very familier with image processing techniques in which mostly
Butterworth and Gaussian bandpass filters are used. However, it seems
that 1D dsp is more concentrated on different filter types than in 2d dsp.
Any enlightenment please.
Isaac
|
I haven't the inclination or endurance to write a treatise on filters,
so here are a few highlights. Recall that most high- and band-pass
filters are derived from low-pass prototypes, so most of the math can be
about the latter. The raised-cosine filter is best treated as an
exception. Let's start with it.
It's main reason for being is that of those filters which eliminate
inter-symbol interference is digital transmissions, it is the simplest
to describe and specify. It would be unsuitable for an IF filter for
radio, TV, or radar. IF filters should have nearly flat tops to preserve
the waveforms of interest, surrounded by steep sides to reject adjacent
channels. In the overall scheme of filters, "raised cosine" is an
unimportant buzzword. <flames redirected to bit bucket>
A naively ideal low-pass filter would pass all frequencies below some
cutoff unchanged, and nothing above that. Aside from the consideration
that such a characteristic is unobtainable, even an approximation to it
has characteristics undesirable for many applications. Such filters
exhibit ringing when excited by signals that have sharp edges.
Since no filter is ideal, various compromises are appropriate in
different circumstances. All of the classical types are based on analog
design and are only approximated by the digital versions that bear their
names. There cam be more than one digital approximation to an analog
type, expanding the list almost to the point of unmanageability. I'll
mention a few analog types briefly.
Filters are characterized not only by type, but also by order. Their
responses are described by fractions that are the ratio of complex
polynomials. The order of the highest polynomial is the order of the
filter; the order of the numerator does not exceed that of the
denominator but can be less.
Butterworth filters are designed by setting as many derivatives to zero
as the degrees of freedom bestowed by the order allow. They are
"maximally flat" in frequency. The distortion they produce in the shape
of rectangular pulses is moderate, as is their cut-off steepness.
Chebychev (Type I) filters use their degrees of freedom to distribute
zero-slope points along the response curve. This creates ripple but
extends the more-or-less flat region to higher frequencies. More ripple
allows steeper cutoff. In the limit of no ripple, it degenerates to
Butterworth. The distortion they produce in the shape of rectangular
pulses is more or less severe depending on the ripple, and their cut-off
steepness is high. (Type II Chebychev filters have the ripple moved from
the passband to the stopband.)
The pulse distortion of these filters is associated with, in one way to
look at the matter, differential delay that depends on frequency. Bessel
filters minimize differential delay, thereby achieving excellent
time-domain response. Naturally, their frequency response suffers.
So much for the analog prototypes. Digital filters can eliminate
differential delay altogether and be as flat and as sharp as you like.
The price paid, aside from computational complexity, is overall delay.
There are several good books that include much accessible detail about
digital filters. You can find a list and other good stuff at
http://www.dspguru.com/info/tutor/index.htm and
http://www.dspguru.com/info/books/index.htm
Jerry
--
You know that the outhouse is in the right place if öżö
it seems too close in summer and too far in winter. ş
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Eric Jacobsen
Guest
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| Posted:
Fri Dec 17, 2004 1:27 am Post subject:
Re: Bandpass filter techniques |
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On Thu, 16 Dec 2004 13:26:14 -0500, Isaac Gerg
<isaac.gergNOSPAM@adelphia.net> wrote:
| Quote: | I am very comfortable with the mathematics behind filtering. I am just
looking for a high level view of the 3 filters I listed. It has been
some time since I have done 1D signal filtering and just inquiring as to
why one would want to use oen filter over another (e.g. Why doesnt
everyone just use a raised cosine filter).
I am very familier with image processing techniques in which mostly
Butterworth and Gaussian bandpass filters are used. However, it seems
that 1D dsp is more concentrated on different filter types than in 2d dsp.
Any enlightenment please.
Isaac
|
The answer to what filter may fit best is very application dependant.
Some applications are very sensitive to the phase response of the
filter, others are not, some require steep transition bands, others do
not, etc., etc.
Do you have an application in mind?
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org |
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Isaac Gerg
Guest
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| Posted:
Fri Dec 17, 2004 1:33 am Post subject:
Re: Bandpass filter techniques |
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Thanks Jerry.. The first paragraph was teh answer I needed. Your
analysis was also must appreciated.
Isaac |
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Andor Bariska
Guest
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| Posted:
Fri Dec 17, 2004 5:07 pm Post subject:
Re: Bandpass filter techniques |
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Jerry Avins wrote:
....
| Quote: | I haven't the inclination or endurance to write a treatise on filters ..
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Still, nice treatsie! |
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Jerry Avins
Guest
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| Posted:
Fri Dec 17, 2004 10:50 pm Post subject:
Re: Bandpass filter techniques |
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Andor Bariska wrote:
| Quote: | Jerry Avins wrote:
...
I haven't the inclination or endurance to write a treatise on filters ..
Still, nice treatsie!
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Thanks. That was barely getting started! To top it off, the OP wrote
that the first paragraph was enough. Can't win!
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Rune Allnor
Guest
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| Posted:
Sun Dec 19, 2004 6:00 pm Post subject:
Re: Bandpass filter techniques |
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Jerry Avins wrote:
| Quote: | I haven't the inclination or endurance to write a treatise on
filters, |
[... excellent treatise snipped ...]
Ehmm... it would be very interesting to see what would come out of
it if you ever wrote such a thing "for real"...
Rune |
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Jerry Avins
Guest
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| Posted:
Sun Dec 19, 2004 6:23 pm Post subject:
Re: Bandpass filter techniques |
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Rune Allnor wrote:
| Quote: | Jerry Avins wrote:
I haven't the inclination or endurance to write a treatise on
filters,
[... excellent treatise snipped ...]
Ehmm... it would be very interesting to see what would come out of
it if you ever wrote such a thing "for real"...
Rune
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I might have mentioned that, whereas the poles of a Butterworth lie
equally spaced on a semicircle, those of a Chebychev Type I lie on a
semiellipse (the semidiameter on the real axis is shortened) but are
otherwise similarly arrayed; that a Butterworth's transfer function has
only one variable term (that, in the denominator) and the exponent of
that term is the order of the filter; and ...
But I'm not writing that treatise, am I?
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Rune Allnor
Guest
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| Posted:
Sun Dec 19, 2004 6:33 pm Post subject:
Re: Bandpass filter techniques |
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Jerry Avins wrote:
| Quote: | Rune Allnor wrote:
Jerry Avins wrote:
I haven't the inclination or endurance to write a treatise on
filters,
[... excellent treatise snipped ...]
Ehmm... it would be very interesting to see what would come out of
it if you ever wrote such a thing "for real"...
Rune
I might have mentioned that, whereas the poles of a Butterworth lie
equally spaced on a semicircle, those of a Chebychev Type I lie on a
semiellipse (the semidiameter on the real axis is shortened) but are
otherwise similarly arrayed; that a Butterworth's transfer function
has
only one variable term (that, in the denominator) and the exponent of
that term is the order of the filter; and ...
But I'm not writing that treatise, am I?
|
I don't know. Are you? Nevertheless, it's always fun to read stuff
from people who are capable of presenting complicated stuff in
both succinct, comprehensable and precise ways.
Rune
Rune |
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