A Technique for Efficient Realization of Wide-Band FIR LTI Systems

This correspondence introduces a technique for efficient realization of wide-band finite-length impulse response (FIR) linear and time-invariant (LTI) systems. It divides the overall frequency region into three subregions through lowpass, bandpass, and highpass filters realized in terms of only one filter. The actual function to be approximated is in the low- and high-frequency regions realized using periodic subsystems. In this way, one can realize an overall wide-band LTI function in terms of three low-cost subblocks, leading to a reduced overall arithmetic complexity as compared to the regular realization. A systematic design technique is provided and a detailed example shows multiplication and addition savings of 62% and 48%, respectively, for a fractional-order differentiator with a 96% utilization of the bandwidth. Another example shows that the savings increase/decrease with increased/decreased bandwidth.