High-speed digital filtering: Structures and finite wordlength effects

Abstract

This paper is a study of high-throughput filter structures such as block structures and their behavior in finite precision environments. Block structures achieve high throughput rates by using a large number of processors working in parallel. It has been believed that block structures which are relatively robust to round-off noise must also be robust to coefficient quantization errors. However, our research has shown that block structures, in fact, have high coefficient sensitivity. A potential problem that arises as a result of coefficient quantization is a periodically time-varying behavior exhibited by the realized filter. We will demonstrate how finite wordlength errors can change a nominally time-invariant filter into a time-varying system. We will identify the block structures that have low coefficient sensitivity, and develop high-speed structures that are immune to the time-varying problems caused by coefficient quantization.

High-speed recursive digital filters based on the frequency-response masking approach

“…However, as increases the complexities of the new filters and the scattered lookahead filters increase rapidly, whereas for the clustered lookahead filters, the complexity increases slowly. 6 On the other hand, algorithm transformation techniques are based upon pole-zero cancellations, which have potential drawbacks under finite-arithmetic conditions [9], [10]. In addition, the clustered lookahead technique requires that the filters be realized with direct-form structures, which generally have problems under finite-arithmetic conditions, especially when stability is concerned [28].…”

“…To the former belong the well-known clustered and scattered lookahead techniques and block realization; see, e.g., [6]- [8] for a review and a comprehensive reference list. Algorithm transformation techniques are based upon pole and zero cancellations, which can be achieved theoretically, but under finite-arithmetic conditions, the cancellations become inexact, which may impose problems such as increased coefficient sensitivity and time-variant behavior [9], [10]. Pole and zero cancellations can be circumvented by using constrained filter-design techniques in which the denominator polynomial of the transfer function is restricted to be a function of .…”

Filter structures composed of all-pass and FIR filters for interpolation and decimation by a factor of two

“…Further, look-ahead filters are based on pole and zero cancellations. When the filter coefficients are quantized, these cancellations become inexact which may impose problems [28], [29]. For the new structures, such problems do not exist.…”

Single Filter Frequency Masking High-Speed Recursive Digital Filters

“…The loop(s) that determine the maximal sample frequency is called the critical loop(s). From (1) we see that the maximal sample frequency can be increased either by increasing the number of delay elements in the loops or by decreasing the total latency of the operations. We want to increase the maximal sample frequency for two main reasons: for high-speed applications, naturally, but also for low-power applications, as any excess speed can be traded for a lower power consumption by decreasing the power supply voltage [2].…”

“…Among the algorithm transformation techniques are scattered look-ahead, clustered look-ahead, and block processing [14]. These are based on pole-zero cancellations, which become inexact under finite-arithmetic conditions and may lead to time-varying behavior and higher coefficient sensitivity [1]. These problems can be avoided by using constrained filter design techniques.…”