Block digital filter structures and their finite precision responses

As VLSI design technology advances, the potential advantages of block filters are shifted from savings in 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 various scalar filter structures to block filter structures and investigate the frequency responses of their finite precision implementations. Since block filters with quantized coefficients are usually periodically time-varying, the errors are described using bifrequency representations. It is known that block filters have reduced round-off noise since the poles are moved toward the origin (thus away from the unit circle), Under coefficient quantization, however, deviations from the desired filter functions are larger for block filters than their scalar counter parts since the poles as well as zeros are more clustered. Therefore, in general, the filter coefficients need higher precision in the block filter implementations. Through computer simulations on the various block filter structures, frequency magnitude responses of their finite precision implementations are investigated.