find information on Tcebysceff(Chebyshev) and Bessel filters, stating the major
differences in output response between these and butterworth design

Hi,

Thanks for your question.

First some definitions:

Roll off: transistion from the pass band to the stop band
equiripple: an oscillation with frequency equally above and below a
mean value
group delay: the negative rate of change of phase with frequency.
Expressed in seconds

I hope I have defined everything that you might not know in the
following answer. Various other filter term definitions are here:
http://members.ozemail.com.au/~timhoop/glossary.htm

Information on the three types of filters:

Chebyshev filters:
* is an amplitude filter
* based on the chebyshev polynomials
* carried out via recursion (rather than convolution). This makes them
faster than filters such as the windowed sinc
* based on the z - transform
* achieves a fast roll off by allowing an equiripple in the frequency
response - the more ripple, the faster the roll off.
* chebyshev poles lie on an ellipse in the complex plane
* come in 2 types - 
      type I: equiripple in the pass band and monotonic in the stop
band. The poles of a type I chebyshev filter are evenly spaced about
an ellipse in the left half plane.
      type II: monotonic in the pass band and an equiripple in the
stop band (type II filters are seldom used) The poles of a type II
chebyshev filter are evenly spaced about an ellipse in the right half
plane.
   (filters with a ripple in both the stop and pass band are called
elliptic filters)
* to design a chebyshev filter, you need to know 4 things:
      1. low pass or high pass response
      2. cut off frequency
      3. % ripple in the passband
      4. number of poles
* has a non linear phase response
* in the time domain, Chebyshev filters overshoot and ring
significantly

Bessel filters:
* is a phase filter
* highly linear phase response 
* constant group delay across the entire passband
* little overshoot and ringing in the time domain
* rolls off monotonically in the stop band
* relatively slow attenuation in the transition-band 
* no ripples

Butterworth filters:
* is an amplitude filter
* based on very simple polynomials
* this is a chebyshev filter with the ripple set to 0% - ie they have
no ripple
* butterworth poles lie on a circle in the complex plane
* maximally flat in the pass band frequency response
* There is some overshoot and ringing in the time domain, but less
than Chebyshev

Major differences in output response:

Chebyshev vs Butterworth:
* Chebyshev rolls off faster than the butterworth filter eg A
chebyshev filter with a ripple of 0.5% has an almost flat passband but
has a much better roll off when compared to a butterworth filter see
figure 20-1 http://www.innerlighttheory.com/ch20.pdf
* Chebyshev has ripples in either the pass or stop band - Butterworth
is monotonic
* Butterworth has less ringing and overshoot in the time domain than
Chebyshev

Bessel vs Butterworth:
* Butterworth rolls off faster than the Bessel filter
* Bessel has a more linear phase response

I hope this answers your question. If it doesn't, or you want me to
explain more my answer or you require equations etc, please request a
clarification.

Thanks,

Jenjerina-ga


Useful links:
This is a chapter 20 of "The Scientist's and Engineer's guide to
Digital Signal Processing" the chapter is called "Chebyshev Filters"
http://www.innerlighttheory.com/ch20.pdf

Frequency Devices' information on the 3 types of filters. Includes
formulas and graphs
http://www.freqdev.com/guide/amp_phase.html

A chapter on filters
http://www.delsys.com/library/papers/fund5.pdf

Google's cache of somebody else's filter study. I have found this to
be accurate and well organised.
http://216.239.53.100/search?q=cache:fWMlSjD66qkC:www.tantalophile.demon.co.uk/linmodem/jamie/NOTES+Chebyshev+filters&hl=en&ie=UTF-8

A site where you can enter parameters to gain the coeffiecents, poles,
zeros, impulse response, step response, magnitude and phase response
etc of the butterworth, bessel and chebyshev filters
http://www-users.cs.york.ac.uk/~fisher/mkfilter/trad.html

Matlab code to produce your own filters:
http://www.ee.ed.ac.uk/~bernie/DSP_SOFT/


Search techniques:
google search with keywords: Chebyshev filters
google search with keywords: Butterworth filters
google search with keywords: Bessel filters

There are three variables that you must understand before comparing
these filter types. Firstly there is passband ripple, this is the
deviation in amplitude from a level response in the passband of the
filter. Secondly there is the settling time of the filter, this being
the time taken for the amplitude of the output to settle at its final
value. Finally there is roll off, which is the steepness of the
passband to stopband transition (or skirt) when viewed in the
frequency domain.
	In terms of these parameters the relative performance of each of the
filter types may be summarised as follows:

BESSEL: 	*Fastest settling time
		*Least passband ripple
		*Shallowest roll off into stop band

CHEBYSHEV: 	*Slowest transient settling time
		*Most passband ripple
		*Steepest roll off into stop band
N.B. It is possible to compromise more passband ripple for a shallower
roll off (and vice versa).

	The Butterworth filter is in between the other two filter types in
terms of performance allowing compromise between settling time, roll
off and passband ripple.