Abstract
The coefficient values and number representations of digital FIR filters have significant impacts on the complexity of their VLSI realizations and thus on the system cost and performance. So, making a good tradeoff between implementation costs and quantization errors is essential for designing optimal FIR filters. This paper presents our complexity-aware quantization framework of FIR filters, which allows the explicit tradeoffs between the hardware complexity and quantization error to facilitate FIR filter design exploration. A new common subexpression sharing method and systematic bit-serialization are also proposed for lightweight VLSI implementations. In our experiments, the proposed framework saves 49%~ 51% additions of the filters with 2's complement coefficients and 10%~ 20% of those with conventional signed-digit representations for comparable quantization errors. Moreover, the bit-serialization can reduce 33%~ 35% silicon area for less timing-critical applications.
Highlights
Finite-impulse response (FIR) [1] filters are important building blocks of multimedia signal processing and wireless communications for their advantages of linear phase and stability
Because few coefficients have more than three nonzero terms after signeddigit encoding and optimal scaling, we propose the SCSAC elimination for the sparse coefficient matrices to remove the common subexpressions across shifted coefficients
Our results show that bit-serialization saves 58% and 53% areas of the adder trees, which turns into 35% and 33% saving on the overall areas, for the 42-tap and 62-tap filter examples, respectively
Summary
Finite-impulse response (FIR) [1] filters are important building blocks of multimedia signal processing and wireless communications for their advantages of linear phase and stability. Some researchers suggested to first design the optimum real-valued coefficients and quantize them with the consideration of filter complexity [24,25,26,27,28,29] We call these approaches the quantizationbased methods. Li’s approach [28] offers the explicit control over the total number of nonzero digits in all coefficients His approach does not consider the effect of CSE and could only roughly estimate the addition count of the quantized coefficients, which might be suboptimal. Our approach can achieve better filter quality with fewer additions, and more importantly, it can explicitly control the number of additions This feature provides efficient tradeoffs between the filter’s quality and complexity and can reduce the design iterations between coefficient optimization and computation sharing exploration.
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