Method of designing digital band-pass filters with pulse response of finite duration

A design method is proposed for narrow-band-pass filters with finite pulse response duration, such filters being used for digital processing of signals such as linear frequency selection. It is based on the use of 2-stage or multistage combs rather than on conventional direct convolution or on secondary discretization (decimation) with subsequent interpolation of output readings. In the 2-stage case the design reduces essentially to synthesis of an equivalent low-pass filter with appropriate frequency selectivity. The number of multiplications per discretization period, which decreases with decreasing bandwidth of the main stage but increases with decreasing bandwidth of the smoothing stage, can be reduced by successive addition of stages. Such filters can be realized with components of one type having identical pulse response characteristics and with a significant reduction of the noise level. The inevitable attendant nonuniformity of amplitude-frequency characteristics can be avoided by optimizing a 2-stage design instead. This method is free of errors inherent in order methods.