"Jerry Avins" <jya@ieee.org> wrote in message news:dK2dnaxul_zRKpbfRVn-1Q@rcn.net...> Bhaskar Thiagarajan wrote: > >> "Triff" <neverread@yahoo.com> wrote in message > > ... > >>>question but what use to chebushev filters have!? >> >> >> Chebychev filters are just one type of filter. >> Filters in general, as the name implies, are used to filter out unwanted >> frequencies. A low pass filter passes all frequencies lower than a >> certain >> cut-off (Fc). A band-pass filter passes all frequencies in a certain >> 'band' >> (F_low and F_high). You can extend this to what high-pass filters are. >> One can build these types of filters using various architectures and >> various >> 'equations' that govern their shape in the frequency domain. Some of >> these >> equations have names (Chebychev, Butterworth, etc) since some dudes were >> the >> first to raise their hand and say "I've got a new one fellas". >> Filters are used in all kinds of applications including sound/audio >> processing, video processing, image processing, digital communications, >> etc > > More specifically, Chebyshev filters allow ripple in the passband in > order to achieve sharper and steeper stopbands. Chebychev himself never > heard of signal processing, but he invented a method of forcing > approximations to have equal-magnitude ripples.Filters are often designed first (in general) by stating an objective criterion or desired response D(x). This can be a general specification such as lowpass, highpass, etc. and then, later, the user of the method can select some filter parameters - like the cutoff frequency. Then the formulator of the method choses some algebraic formulation using some set of functions like: A(x)=a +bx +cx^2.... or A(x)=a1 +b1cos(x) +b2sin(x) +c1*cos(x) +c2sin(x) +d1*cos(2x) +d2*sin(2x) .... to represent the design that *approximates* D(x). The design task is to find the coefficients a,b,c..... so that some function of the error [D(x)-A(x)] is minimized. So, the formulator figures this out and the end designer just needs to use the method. A common function of the error is sum over x of [D(x)-A(x)]^N where N is generally an even integer so that the measure is always positive. You can see that as N gets bigger, the highest peak of D-A is emphasized more. With most approximation situations the Chebyshev approach means that you are minimizing the maximum error - as measured against the objective criterion or desired filter response that is stated up front. No other filter of the same order can have a smaller peak error. This is known as the minimax or L-infinity norm (N above is very high)- where the error is weighted so heavily (taken to the power of "infinity" in concept) that all that can happen is the highest peak of the error is minimized. There are other measures like L2 which minimizes the sum of the square of the errors, L1 that minimizes the sum of the errors, etc. There may be a very small difference between L10 and L-infinity..... I believe the original Chebyshev polynomials generated maximally flat passband and minimax / equiripple stopband. Now there are programs that design filters that are minimax in both the passband and stopband and these are sometimes called Chebyshev filters and most often, equiripple. The method to get them works to MINimize the MAXimum error - thus, minimax. So, that's what "Chebyshev", equiripple or minimax means. It has only little to do with the goodness of the filter for any particular application and some other base method might just as readily be used. Fred