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Bandpass filter techniques

Started by Isaac Gerg December 16, 2004
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
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



Isaac Gerg wrote:
> 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
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. �����������������������������������������������������������������������
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
Isaac Gerg wrote:

> 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 &#2013266166;&#2013266111;&#2013266166; it seems too close in summer and too far in winter. &#2013266068;&#2013266106;&#2013266067; &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On Thu, 16 Dec 2004 13:26:14 -0500, Isaac Gerg
<isaac.gergNOSPAM@adelphia.net> wrote:

>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
Thanks Jerry.. The first paragraph was teh answer I needed.  Your 
analysis was also must appreciated.

Isaac
Jerry Avins wrote:
...

> I haven't the inclination or endurance to write a treatise on filters ..
Still, nice treatsie!
Andor Bariska wrote:

> Jerry Avins wrote: > ... > >> I haven't the inclination or endurance to write a treatise on filters .. > > > Still, nice treatsie!
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. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
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