The optimum design of one- and two-dimensional FIR filters using the frequency response masking technique

An expression for the impulse response up-sampling ratio M, which will produce a minimum complexity design, is derived. It is shown that M approaches e (the base of the natural logarithm) as the number of frequency response masking stages increases; in a K-stage design the complexity of the filter is inversely proportional to the (K+1)th root of the transition width; the frequency response masking technique is effective if the normalized transition width is less than 1/16; and the frequency response masking technique is more efficient than the interpolated impulse response technique if the square root of the normalized transition width is less than the arithmetic mean of the normalized passband edge and stopband edge. An expression for the multistage frequency response ripple compensation is derived. An optimum design relationship for the interpolated impulse response technique is also derived. The design of narrow-band two-dimensional filters using the frequency response masking technique is also presented