Robust convolution using data-compression schemes

Abstract

The techniques of differential pulse code modulation (DPCM) and error spectrum shaping (ESS) have been used in many data compression schemes in the past. We propose a novel technique for robust convolution of two signals under finite precision based on the ideas of DPCM and ESS. The proposed structure is much simpler and more efficient compared to traditional low sensitivity FIR structures. It directly exploits signal correlation and impulse response correlation before quantizing to finite precision. We apply both DPCM and ESS techniques to both the input signal and FIR filter coefficients. By using mean square error (MSE) as a measure of figure of merit, we define the coding gain as the ratio of the MSE in direct convolution to the MSE in the system. We show that the coding gain of the DPCM-ESS convolver is the product of the prediction gain of both the input signal and the filter. The method can be applied to linear phase FIR filters to achieve high coding gain while preserving the advantage of linear phase. Examples show that good filters can be obtained by using low bit multipliers. >