FIR Variable Digital Filter With Signed Power-of-Two Coefficients

Variable digital filters (VDFs) are useful for varioussignal processing and communication applications where the frequencycharacteristics, such as fractional delays and cutoff frequencies,can be varied online. In this paper, we investigate the designof VDFs with discrete coefficients as a means of achieving lowcomplexity and efficient hardware implementation. The filter coefficientsare expressed as the sum of signed power-of-two terms witha restriction on the total number of power-of-two for the filter coefficients.An efficient design procedure is proposed that includes animproved method for handling the quantization of the VDF coefficientsfor both the min–max and the least-square criteria leadingto an optimum quantized solution. For the least-square criterion,a reduced search region around the optimum quantized solution isfurther constructed and the branch and bound method in conjunctionwith an efficient branch cutting scheme is presented to searchfor an optimum solution in this reduced region.