Low Power Implementation of Digital Filters using DBNS Representation and Sub-expression Sharing

Abstract

This paper presents a solution for low power consumption in digital systems designs. The Double Base Number System (DBNS) representation recognized by its high sparseness is used for digital filters coefficients representation to reduce the switching activity, a key factor in power consumption.In this paper, we show that the use of the Canonic DBNS representation for filter coefficients representation leads to a dynamic power reduction average of 30% compared to the 2's complement representation. The second contribution of our work consists in the application of sub-expression sharing on the filter coefficients, already expressed in DBNS representation. Strengths and limitations of this optimization will be discussed in details throughout this paper.

New Multiplier for a Double-Base Number System Linked to a Flash ADC

“…In the T expression, if the mantissa m of the filter coefficient and ternary 3 t of the digitized signal can be converted into a 2 E format, the multiplication becomes simple. The filter coefficients are in the range of [0, 1), and the mantissa m is in the range of [1,2). The nonlinear value of 2 f is always less than the linear value of m=1+f, where m=1, f=1+f, and f∈[0, 1), in the given ranges as shown in Fig.…”

“…The effectiveness of the DBNS has already been demonstrated in the design of fast DSP systems [1]- [4]. Alternative number systems, including the doublebase number system (DBNS), are often suggested to reduce the complexity of the arithmetic operations because multiplication, which is the dominant operation of DSP, is performed less efficiently in a binary number system.…”

“…Alternative number systems, including the doublebase number system (DBNS), are often suggested to reduce the complexity of the arithmetic operations because multiplication, which is the dominant operation of DSP, is performed less efficiently in a binary number system. The effectiveness of the DBNS has already been demonstrated in the design of fast DSP systems [1]- [4]. When there is only a single DBNS term, the multiplication can be done simply by adding the exponents.…”