Use of radix-r recoding schemes for the realization of multiplier-free FIR filter with periodically time-varying coefficients

The paper introduces a high-precision multiplication-free realization for FIR filters. The realization is based on the use of a linear periodically time-varying (PTV) system together with upsampling and downsampling to achieve time-invariant, multiplication-free FIR. Radix-r recoding schemes are used for obtaining the filter coefficients, which are periodically time-varying. The impulse response samples of the target filter are used to calculate the PTV coefficients. In the radix-r recoding scheme, the values of the PTV coefficients take any value from the set {±2^p, ±(2^p-1), ..., ±2, ±1, 0}, where p=log r-1. These values are either power-of-two or sum of two power-of-two, accordingly, the realizations need only addition/subtraction and shift operations. The use of recoding schemes results in more accurate characteristics and higher precision than the case of using radix-r encoding