Roundoff noise analysis of signals represented using signed power-of-two terms

Multiplierless filtering is very attractive for digital signal processing, for the coefficient multiplier is the most complex and the slowest component. An alternative way to achieve multiplierless filtering other than designing digital filters with signed power-of-two (SPT) coefficient values is to round each input data to a sum of a limited number of SPT terms. However, a roundoff noise representing the roundoff error is introduced when signal data are rounded to SPT numbers. In the SPT space, the quantization step size is nonuniform and thus the roundoff noise characteristic is different from that produced when the quantization step size is uniform. This paper presents an analysis for the roundoff noise of signal represented using a limited number of SPT terms. Roundoff errors for Gaussian distributed inputs are estimated by using our analysis. Examples show that the estimated errors are very close to the actual ones.