Constrained least square design of FIR filters without specified transition bands

We consider the design of digital lters and discuss the inclusion of explicitly speciied transition bands in the frequency domain design of FIR lters. We put forth the notion that explicitly speciied transition bands have been introduced in the lter design literature as an indirect and often inadequate approach for dealing with discontinuities in the desired frequency response. We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR lters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR lters and gives the best L2 lter and a continuum of Chebyshev lters as special cases.