Programmable power-of-two RNS scaler and its application to a QRNS polyphase filter

The scaling operation, i.e. the division by a constant factor followed by rounding, is a commonly used technique for reducing the dynamic range in digital signal processing (DSP) systems. Usually, the constant is a power of two, and the implementation of the scaling is reduced to a right shift. This basic operation is not easily implementable in the residue number system (RNS) due to its non positional nature. A number of different algorithms have been presented in the literature for the RNS scaling. In this paper, several RNS dynamic reduction techniques have been analyzed and the selected one is applied to a polyphase filter bank. A comparison of the filter bank scaled with RNS to binary and binary to RNS conversions, and the RNS scaled implementation is presented. A reduction of area and power consumption of about 30% for the scaling block is obtained.