Implementation Of Recursive Digital Filters Research Articles

Error Spectrum Shaping in Two‐Dimensional Separable‐Denominator Digital Filters

AbstractIn the implementation of recursive digital filters, the characteristics might be degraded due to finite word length effects. The degradation generates noise at the filter output which is caused by roundoff errors in the product quantization. A technique called error spectrum shaping (ESS) can be applied to suppress the noise. ESS usually relies on the use of feedback of roundoff errors and sometimes their feedforward. In this paper, a technique is developed for ESS in two‐dimensional separable‐denominator digital filters by applying both feedback and feedforward of roundoff errors. A two‐dimensional separable denominator is implemented with the minimum number of delay elements and includes two quantizers. A genetic algorithm is also applied to obtain the suboptimal discrete solution of feedback–feedforward coefficients for the purpose of cost reduction. Finally, a numerical example is given to illustrate the utility of the proposed technique. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(4): 10–19, 2002

Pipelined recursive digital filters: a general look-ahead scheme and optimal approximation

A new look-ahead (LA) scheme, distributed look-ahead (DLA), is proposed for pipelined implementation of recursive digital filters. It is established that, in the case of many recursive filters, DLA can provide equivalent and stable implementation with reduced multiplication and latch complexities, and higher area-efficiency. It also produces outputs with reduced delays, when compared with some existing LA schemes. Stability regions for the proposed scheme are also well defined. Next, a time-domain approximation method is proposed for direct design of pipelined recursive filters that can achieve superior match with reduced pipelined filter orders.

直列積分演算要素のディジタル化に関する新手法と直線位相巡回型ディジタルフィルタ実現への応用

直列積分演算要素のディジタル化に関する新手法と直線位相巡回型ディジタルフィルタ実現への応用

Minimisation of computation for digital controllers

A novel Structure is described and analysed which has a number of advantages for the practical implementation of recursive digital filters in control applications. It is based upon the use of an established alternative to the usual z-1 delay operator, but this has been developed into a standard form called a δ filter which is both robust and versatile. The advantages are shown to be in the simplicity of implementation, including the determination of word-lengths for the coefficients and variables. First- and second-order filter structures are given in detail, and simulations presented to demonstrate the operation of a few typical filters. Significant reductions in computation requirements are possible using the δ filter.

Pipeline interleaving and parallelism in recursive digital filters. II. Pipelined incremental block filtering

For pt.I see ibid., vol.37, no.7, p.1099 (1989). Block implementation and fine-grain pipelined block implementation of recursive digital filters are discussed. A new technique of incremental output computation is introduced which requires a linear complexity in block size. Based on the clustered look-ahead and incremental output computation approaches, incremental block-state structure is derived for block implementation of state-space filters of multiplication complexity linear in block size. The incremental block-state structure is also extended for the multirate recursive filtering case. The techniques of scattered look-ahead, clustered look-ahead, decomposition, and incremental output computation are combined to introduce several pipeline stages inside the recursive loop of the block filter. Deeply pipelined block filter structures are derived for implementation of direct-form and state-space-form recursive digital filters. The multiplication complexity of these pipelined block filters is linear with respect to the block size and logarithmic with respect to the number of loop pipeline stages, and the complexities due to pipelining and block processing are additive.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Alternative implementation of systolic recursive digital filters

A new systolic array for the implementation of a recursive digital filter is presented. The operation-delay macrocomponent and the unit delay are the only elements composing the filter architecture. This architecture is fully pipelined and the output can be taken every cycle.

An algorithm for constrained roundoff noise minimization in digital filters with application to two-dimensional filters

An algorithm is presented for minimizing roundoff noise effects in state-space implementations of recursive digital filters while constraining certain coefficients to be zero. Beginning with a direct form structure, the algorithm uses the scaling and noise matrices to iteratively construct an upper or lower triangular transformation matrix to apply to the original state-space model. The result is a structure with a saving of N(N-1)/2 multiples over the minimum noise structure. The technique is of great utility in the realization of two-dimensional filters that cannot, in general, be factored into the parallel or cascade connection of lower-order subfilters. Because of the sparse nature of the local state-space structure coefficient matrices in two-dimensional direct- and controller-form realizations, transforming with an upper and lower triangular block diagonal transformation matrix retains many zeros in the structure and results in a low roundoff noise, computationally efficient state-space realization. A novel controller-form state-space structure for a general two-dimensional function is presented to which the noise minimization procedure is directly applicable. Numerical examples are included. >

Systolic arrays for recursive digital filtering

Two classes of systolic array for the implementation of recursive digital filters are presented, which overcome some of the limitations of earlier designs. The trade-off resulting from varying the degree of pipelining is discussed.

Block implementation of recursive digital filters--New structures and properties

Several new structures for the block implementation of HilR digital filters are proposed. The relation between the pole locations of the block structure to that of the original scalar transfer function is derived. A method to obtain the scalar transfer function from a given block structure is described.

Reducing noise in recursive digital filters by residue retention

This letter describes the application of residue-retention techniques, normally associated with digital differential analysers, to reduce round-off noise within short-word-length implementations of recursive digital filters. Simulations show significant improvements over single- and partial double-precision realisations, especially if high sampling rates are used.

Limit-cycle oscillations in digital filters

A deterministic analysis of limit-cycle oscillations, which occur in fixed-point implementations of recursive digital filters due to roundoff and truncation quantization after multiplication, is performed. Amplitude bounds, based upon a correlated (nonstochastic) signal approach using Lyapunov's direct method, as well as a general matrix formulation for zero-input limit cycles, are derived and tested for the two-pole filter. The limit cycles are represented on a successive-value phase-plane-type diagram from which certain symmetry properties are derived. The results are extended to include limit cycles under input-signal conditions.

Block implementation of digital filters

A theory for implementation of recursive digital filters that process signals by blocks is presented. It is shown that this approach provides a very general family of filters that includes both the conventional scalar implementation and batch processing. The approach is based on a matrix representation of convolution and results in a state-variable description with block feedback. An eigenvalue analysis guarantees stability of the realization and indicates a reduction in sensitivity to roundoff and coefficient accuracy.