An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a signal processing filter with equalized ripple (equiripple) behavior in both the passband and the stopband.
In these notes, we are primarily concerned with elliptic filters. But we will also discuss briefly the design of Butterworth, Chebyshev-1, and Chebyshev-2 filters and present a unified method of designing all cases. We also discuss the design of digital IIR filters using the bilinear transformation method.
Elliptic filters offer steeper rolloff characteristics than Butterworth or Chebyshev filters, but are equiripple in both the passband and the stopband. In general, elliptic filters meet given performance specifications with the lowest order of any filter type.
Elliptic filters, also called “brick wall” filters, have very sharp filter cutoff characteristics. Again, this is done at the expense of a very nonlinear group delay. One flavor of elliptic filters has a zero ripple in the passband but a finite ripple in the stopband.
Introduction Elliptic filters [1–11], also known as Cauer or Zolotarev filters, achieve the smallest filter order for the same specifications, or, the narrowest transition width for the same filter order, as compared to other filter types.
Elliptic Filters • Four degrees of freedom: PB ripple, SB ripple, order, passband edge. • Order of the system controls the transition bandwidth. • Equiripple in both the passband and the stopband. • Elliptic filters are the lowest order rational function approximation to a …
Elliptic filters, also known as Cauer filters, are a type of analog or digital filter characterized by their efficient performance in achieving a specified frequency response with minimal component usage.