FIR variable digital filter with signed power-of-two coefficients

Variable digital filters (VDFs) are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied online. In this paper, we investigate the design of VDFs with discrete coefficients as a means of achieving low complexity and efficient hardware implementation. The filter coefficients are expressed as the sum of signed power-of-two terms with a restriction on the total number of power-of-two for the filter coefficients. An efficient design procedure is proposed that includes an improved method for handling the quantization of the VDF coefficients for both the min--max and the least-square criteria leading to an optimum quantized solution. For the least-square criterion, a reduced search region around the optimum quantized solution is further constructed and the branch and bound method in conjunction with an efficient branch cutting scheme is presented to search for an optimum solution in this reduced region. Index Terms--Finite-impulse response (FIR) variable digital filter (VDF), least-square criteria, min--max, optimization, signed power-of-two (SPT) coefficients.