Method for implementing a multiplier-less FIR filter

Abstract

A method for implementing a multiplier-less FIR filter is disclosed, in which the FIR filter performs the convolution of 1 H ⁡ ( z ) = ∑ k = 0 N - 1 ⁢ ⁢ h k ⁢ z - k , where hk is the k-th coefficient of the FIR filter. The dynamic range of the filter coefficients is compressed by a transformation: 2 H ′ ⁡ ( z ) = H ⁡ ( z ) ⁢ ∏ i = 1 m - 1 ⁢ ⁢ ( 1 + α i ⁢ z - β ) m ∏ i = 1 m - 1 ⁢ ⁢ ( 1 + α i ⁢ z - β ) m , where parameters α and β are chosen depending on filter type, −1≦αi≦1, and m denotes iteration numbers of coefficient operation of transformation, so as to avoid the serious quantization error caused by the phenomenon of SPT distribution. Then, the compressed coefficients are quantized into SPT numbers, and the coefficients are optimized by removing redundant STP numbers.

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