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This paper addresses the problem of implementing narrowband FIR filters using FPGAs. The method uses a tu'nable quadrature sigma-delta modulator to re-quantise a realor complex-valued input stream to a reduced precision, so removing the requirement for a full multiplier in the filter hardware. This makes the technique very attractive for implementation using FPGAs. The re-quantisation process preserves the dynamic range of the signal components contained in the bandwidth of the filter, while shifting the re-quantisation noise to the spectral region to be rejected by the filter. The filter architecture described and its implementation using Xilinx FPGAs is presented. 1 I n t r o d u c t i o n Several methods for field programmable gate array (FPGA) implementation of finite impulse response (FIR) filters have been presented in the literature. Because multipliers are expensive functional units to implement using FPGA technology virtually all of the methods employ techniques that avoid the requirement for a full multiplier. Isoaho [1] uses a shifter based solution, which means that the coefficients are powers of two or combinations of several such components. Mintzer [2] used a distributed arithmetic (DA) [3] approach to implement 1-D filters using Xilinx [4] FPGAs. Data quantised by a uniform quantiser operating at the Nyquist rate is the standard solution to the problem of representing data within a specified dynamic range. Each additional bit of resolution in the quantiser provides an increase in dynamic range of approximately 6 dB. While the required dynamic range of a system fixes the number of bits required to represent the data, it also effects the expense of subsequent arithmetic operations, in particular multiplications. To reduce the logic requirements of the filter, various investigators have explored the design of filters with highly quantised filter coefficients. In this paper an alternative approach to reducing the arithmetic workload is explored in which the the input data is re-quantised using quadrature sigma-delta modulation encoding prior to filtering. This method for implementing a narrow-band FIR filter is based on the observation that good signal fidelity is only required in the spectral region delineated

Fir Filtering with Fpgas Using Quadrature Sigma-Delta Modulation Encoding