A recursive approach to the design of linear-phase half-band digital filters having very sharp transition bands

Linear-phase FIR digital filters having sharp transition bands find a wide variety of applications in modern digital signal processing. By using conventional design techniques, the resulting FIR digital filters require a large number of multiplier coefficients, making their hardware implementation expensive. This paper presents a recursive approach to the design of linear-phase half-band digital filters having very sharp transition bands. It is shown that by embedding a half-band digital filter between proper decimation and interpolation stages, one can make the filter transition band sharper. In this way, a half-band digital filter having a very sharp transition band can be obtained recursively, by starting from a corresponding half-band digital filter with a gradual transition band. The required sharpness can be achieved by increasing the number of recursions.