Internal quantization in FIR filters implemented using Multiple Constant Multiplications

This paper introduces an approach for quantizing intermediate values within an Multiple Constant Multiplication (MCM) implementation of a finite impulse response (FIR) filter. For a fixed-point Digital Signal Processing implementation, finite wordlength behavior in digital filter is very important. We proposed an approach to reduce the quantization noise at the filter output while maintaining performance and keeping space requirements low. This approach is based on calculating the sensitivity of each node. By selectively adding 2 more bits to the high sensitivity nodes to store intermediate information for a 22^nd order half-band filter, the final output noise of FIR filter is reduced up to 40%. Considering the error distribution after each operation provides insight into the effects of quantization.