Effects of Coefficient Quantization in Block Filters

Abstract

VLSI의 설계 기술이 발전함에 따라 블록 필터의 설계는 FFT를 이용한 계산의 수를 줄이는 것으로부터 병렬 계산쪽으로 관심을 가지게 되었다. 왜냐하면 적합한 블록 필터의 설계는 계산 속도면에서나 수치 정확도면에서 바람직한 결과를 얻을 수 있기 때문이다.

본 연구에서는 스칼라 필터를 블록 필터로 변환하는 과정을 설명하고, 특히 정밀도가 높은 블록 상태공간 필터와 블록 래티스 필터에 대하여 블록 필터 계수의 양자화 효과를 비교하였다.

As VLSI design technology advances, the potential advantages of block filters are shifted from the savings of the number of computations(using FFT) to computational parallelism. Since fixed point finite precision arithmetic is preferred in high throughput digital signal processing systems, the use of proper block filter structures with good numerical properties is desirable.

In this paper, we extend scalar filter structures to block filter structures and investigate their coefficient quantization effects. Since block filters with quantized coefficients are usually periodically time-varying, the errors are described using bi-frequency representations.

Under coefficient quantization, however, deviations from the desired filter functions are larger for block filters than scalar counter parts since poles and zeros are clustered more closely. Therefore, in general, the filter coefficients need higher precision in the block filter implementations. Through computer simulations of the various block filter structures, finite coefficient quantization properties are investigated.

As VLSI design technology advances, the potential advantages of block filters are shifted from the savings of the number of computations(using FFT) to computational parallelism. Since fixed point finite precision arithmetic is preferred in high throughput digital signal processing systems, the use of proper block filter structures with good numerical properties is desirable.

In this paper, we extend scalar filter structures to block filter structures and investigate their coefficient quantization effects. Since block filters with quantized coefficients are usually periodically time-varying, the errors are described using bi-frequency representations.

Under coefficient quantization, however, deviations from the desired filter functions are larger for block filters than scalar counter parts since poles and zeros are clustered more closely. Therefore, in general, the filter coefficients need higher precision in the block filter implementations. Through computer simulations of the various block filter structures, finite coefficient quantization properties are investigated.