Multiplierless implementation of bandpass and bandstop recursive digital filters using low-sensitivity transformation

Multiplierless filters are natural extensions of the low-sensitivity structures. Some low-sensitivity transformations are investigated for converting a prototype lowpass filter into a bandpass or a bandstop filter. The resulting coefficient values, due to such transformations, become quite low compared with conventional structures. When the coefficient values are expressed in minimum signed powers of two (MNSPT) forms or canonic signed digit (CSD) forms, they require few shifts and adds and/or subtracts for implementation and a multiplierless realization can be obtained. Further, when we allow some marginally insignificant deviation in the specifications including the tolerances and the bandedges, the number of shifts and adds and/or subtracts per multiplier becomes quite small making this approach quite attractive. Alternatively, we can design the overall filter with marginally stricter tolerances than the desired specifications and meet the criteria after quantizing the coefficients.