Digital Filter Transfer Research Articles

Performance evaluation of infinite impulse response filter synthesis using parallel-Direct-Ladder form under finiteword-Length effects

Synthesizing a parallel-form IIR filter from a given non-strictly-proper transfer function requires a polynomial long division method, which results in dynamical range problem under finite word-length (FWL) fixed-point implementations. Based on the state-space similarity transformation, in this paper, a synthesis scheme for parallel-form IIR filters is proposed without requiring long division of polynomials operations to reduce dynamical range problems for obtaining parallelized first or second-order sections either in direct-form or coupled-form. The main advantage of the proposed scheme is that the parallelized IIR filter can be synthesized based on state-space normal-form similarity transformation from any digital filter transfer functions. In addition, the proposed two modified coupled-form filters based on the parallelized IIR filter have benefits of less computational consumption and zero-input limit-cycle free, especially for modified second-order coupled forms in contrast with the conventional coupled-form biquad. Finally, two numerical examples are performed to illustrate the effectiveness of the proposed scheme.

Optimization of digital filters performances simultaneously in frequency and time domains

Wide used method of digital filters design consists in transformation of analog filter-prototype with required performances into digital filter. This method is applicable if the transformation preserves optimality of filter performances under specified set of quality indexes (QI). It was denoted earlier that such situation is possible when gain-frequency response (GFR) and phase-frequency response are optimized simultaneously. The task of simultaneous optimization of digital filters GFR and step response (SR) is also important but yet a little explored. Alternative method of this problem solving consists in search of digital filter transfer function (TF) which is optimal under GFR and SR QI’s. To investigate capabilities of the first method we found examples of analog filters Pareto-optimal under rise time and transient duration. Other QI’s of these filters fulfilled specified constraints. Then these filters were transformed into digital filters. Bilinear transformation and transformation with invariant impulse response were applied. Further we did the search of digital filters optimal under the same set of QI’s. In either method the hybrid heuristic algorithm was applied for search optimal solutions in the space of TF poles and zeroes coordinates. The results of investigation demonstrated that digital filters developed via search are superiorly under specified set of QI’s then digital filters developed via transformation of analog filters. Accordingly Pareto-optimality for QI of GFR and SR is not preserved during such transformation and direct search must be applied to optimized digital filters simultaneously in frequency and time domains. Further in some cases analog filters developed via reverse bilinear transformation of the found optimal digital filters are superiorly under the same set of QI’s then analog filters developed using search. In such cases using of digital filter-prototypes for design of analog filters is practical.

Converting Series Biquad Filters Into Delayed Parallel Form: Application to Graphic Equalizers

Digital filter transfer functions can be converted between the direct form and parallel connections of elementary sections, typically second-order (“biquad”) sections. The conversion from direct to parallel form is performed using a partial fraction expansion, which usually requires long division of polynomials when expanding proper and improper transfer functions. This paper focuses on the conversion of a series of biquad sections to the parallel form, and proposes a novel way to implement the partial-fraction expansion without the use of long division. Additionally, the resulting structure is the delayed parallel form in which the section gains remain small. The new design and previous methods are compared in a case study on graphic equalizer design. The delayed parallel filter is shown to use the same number of operations as the series form during filtering. The conversion of a recently proposed series graphic equalizer into the delayed parallel form leads to an improved parallel graphic equalizer design relative to all known prior approaches. The proposed conversion technique is widely applicable to the design of parallel infinite impulse response filters, which are becoming popular as they are well suited to implementation using parallel computers.

Grey Wolf Optimizer Driven design space exploration: A novel framework for multi-objective trade-off in architectural synthesis

Abstract Initiating Design Space Exploration (DSE) procedure during architectural synthesis is a highly intricate and tedious process. It involves optimal arrangement of resource utilizations within a design search space to resolve conflicting objectives of power-performance as well as area occupied by different types of resources. To arrive at an arrangement with minimum completion time among all of the permuted arrangements is a Non-Polynomial-hard problem. The problem becomes acute when it involves multi-objectives, as in the case of DSE for ensuring reliable power-performance-area trade-off of application specific processors. Many heuristic algorithms are being considered to derive an optimal solution for this multi-objective DSE procedure. A comprehensive mapping process and reliable solution evaluation approach called Grey Wolf Optimizer Driven DSE (GWO-DSE) is proposed in this article. The contributions of the article are as follows: i) Introduction of a novel GWO-DSE methodology for power-performance-area trade-off ii) Unique solution evaluation methodology called Utility Coefficients and Utility Ranking iii) Unique fitness evaluation function Grey wolf optimizer iv) Comparative benchmarks using digital filter transfer functions v) Substantial improvement in solution arrival within search space (average > 51%) and reduction in exploration time (>89%) when compared to recent DSE approaches for the tested benchmarks.

English

The proposed research work on the topic Infinite Impulse Response Structure and Its Application is basically state space representation for the digital filter of different form obtained from analog filter and transformation to digital one. In the normal course of analysis the digital filter transfer function are realized in different forms using time delay elements and multipliers. This realization can be eased if digital filter are represented in state space techniques opening a new field for computation analysis. This aspect has been incorporated in the proposed research work things outlining the introduction of IIR filter and different structure including ladder and wave structure realization, state space description of IIR filter is presented in detail including the normal form which has complex structure but simple form of state equation. IIR filter design is based on state space technique using Lattice structure. The generalized technique of state space equation realized from general form of digital filter transfer function has been developed then the technique is demonstrated using differential form of various filter like LPF, HPF and BPF for the required order of analog filters. Statistical analysis of digital filter like round off error and dynamic scaling has been incorporated, where the two direct computes have been lumped together in the common state space representation. Autocorrelation and uncorrelation between noise and input samples gives round off noise and dynamic scaling give expression for the factor forms, round off error and dynamic range. This aspect on statistical analysis of digital filter has opened a new field for research.

The design of two channel IIR QMF bank directly from analogue prototype

This article presents a new method for designing two-band quadrature mirror filter (QMF) banks. Analytic solution of the filter coefficients is obtained in the s-domain. The characteristic function of the new filter has one multiple pole in the pass-band and one multiple zero in the stop-band. As a consequence, the transfer function has a single ripple, both in the pass-band and in the stop-band. Lowpass and highpass filter pair is double complementary in the s-plane. The gain responses of the lowpass and highpass filter pair at the crossover frequency are approximately 3 dB below their maximum values. Using the bilinear transformation, the analogue filter transfer function is mapped into the corresponding digital filter transfer function, so that the analogue crossover frequency is mapped into the digital frequency corresponding to ω = π/2. The filter characteristic exhibits Butterworth-like behaviour near the origin and Chebyshev-like behaviour (of the third order) near the pass-band edge.

Equiripple minimum phase FIR filter design from linear phase systems using root moments

In this brief we propose to design a minimum phase finite-impulse response (FIR) digital filter transfer function from a given equiripple linear phase FIR transfer function which has identical amplitude. The brief deals with two important issues. The first issue is that we are concentrating on very high degree polynomials for which factorization procedures for root extraction are unreliable. A novel approach is taken, that involves the use of a set of parameters called root moments of a polynomial, derivable directly from the polynomial coefficients that immensely facilitate the factorization of polynomials of very large order. The second issue is that the polynomials we deal with have roots on the unit circle. In the paper we propose a method to overcome this problem. The results of the proposed design scheme are very encouraging as far as robustness and computational complexity are concerned.

Pipelining of IIR digital filters

In this paper, we propose to present the direct fonn recursive digital filter as a state space filter. Then, we apply a look-ahead technique and derive a pipelined equation for block output computation. In addition, we study the stability and multi­ plication complexity of the proposed pipelined-block implementation and compare with complexities of other methods. An algorithm is derived for the iterative computation of 1. Introduction. Digital filter transfer function theoretically can be realized in an infinite number of ways. From the standpoint of implementation, some structures may be of lower complexity, while others may be pipelinable, and yet some others may consist of regular modules that can save design time. Much research has been carried out in search of different realization structures with various desirable properties and enhanced performance. Achieving high speed in recursive direct-form filters is difficult because of the feedback loop (Chung and Parhi, 1994). High performance in very large scale integration (VLSI) circuits can be achieved by using high speed technologies without modifying the algorithm. On the other hand, we can use a low cost technology and gain an impressive performance by exploiting concurrency. Concurrent structures can be derived by implementing the existing algorithms in new ways. We do not change the transfer function of the filter, but we do change the internal structure of the filter (Parhi and Messerschmitt, 1989). Pipelining and block processing are two of several algorithmic transformation techniques that can be used to exploit the concurrency within a digital signal processing algorithm to improve its operat­ ing speed or reduce the number of resources required in a parallel processing environment (Lucke and Parhi, 1994). Pipelining (Chung and Parhi, 1994; Parhi

Design and implementation of efficient pipelined IIR digital filters

A generalized clustered look-ahead transformation procedure is presented. Like the original clustered look-ahead transformation, the generalized version is useful for converting IIR digital filter transfer functions into pipelined forms. It is, however, better able to yield stable pipelined IIR filters. It is shown that this improvement is obtained at the expense of a very modest increase in system complexity and a small decrease in processing speed. Design examples are given and high-speed hardware implementations are discussed in detail.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A dedicated processor for time-varying digital audio filters

A dedicated processor for realizing variable digital filters suitable for audio applications is presented. Its architecture is based on the approximation of the time-varying system by finite number of invariant states. A technique which reduces digital filter transfer function distortions caused when filter parameters are changed over time is employed. The proposed transition model is realized by a dedicated unit having a pipeline architecture and allowing a very large number of variable filters to be implemented in real-time. >

Realization of 2-D denominator-separable digital filter transfer functions using complex arithmetic

In this paper the problem of realizing 2-D denominator-separable digital filter transfer functions is considered for processing of real sequences. The approach is based on expressing the given 2-D transfer function as a sum of two reduced-order rational transfer functions with complex coefficients. New structures are obtained for equivalent reduced-order, complex-coefficient, 2-D transfer functions. All the realizations are basically parallelform structures with minimum-norm, low round-off noise and freedom from overflow limit cycles. A comparison of the different structures is also made.

Deblurring of digital images through a spatial domain approach

A spatial domain technique for restoring out-of-focus images, with a minimum a priori knowledge about the Point-Spread Function (PSF) of the imaging system, is presented. In the proposed algorithm an estimate of the spatial constant (σ) of the Gaussian PSF is obtained, which is then utilized to calculate in a least-squares sense a corresponding 2-D recursive (IIR) digital filter transfer function. This filter is then used to restore the blurred image. This procedure is applied to different blurred images, and the results obtained demonstrate the effectiveness of the method.

Computer-aided analysis of wave digital filter transfer characteristic

An approach for finding the wave digital filter transfer characteristic is developed with a general computer program. The program can be used to analyse the quantification effect of different multiplier coefficient wordlengths for the wave digital filter transfer characteristic, thus it is possible to make a reasonable choice of coefficient word-length in order to take account of economization as well as technical specifications when the wave digital filter is in hardware implementation.

The necessary and sufficient conditions for minimum roundoff noise in second-order state-space digital filters and their optimal synthesis

For second-order state-space digital filters, new expressions for the covariance matrix K and the unit noise matrix W are derived. Using these, the necessary and sufficient conditions for minimum roundoff noise in scaled filters are given in terms of the state parameters. Simple expressions for the second-order modes of the filter and for the attainable lower bound of the unit noise gain are provided. The scaled state realizations having minimum roundoff noise are evaluated for all types of digital filter transfer functions using only their coefficients.

Generalized approximation techniques for selective linear-phase digital and nonreciprocal lumped filters

The paper presents expressions for low-pass digital filter transfer functions with finite-band approximation to constant amplitude and delay in the passband, together with an arbitrary number of transmission zeros at half the sampling frequency. The corresponding high-pass filter transfer functions can be obtained by a transformation. The available degrees of freedom can be divided arbitrarily between the passband and stopband responses. The functions are of the nonminimum-phase type, and the corresponding nonreciprocal analog (continuous) filters are also covered; these can be realized in standard active RC structures. The zero-bandwidth cases are obtained, either directly or as limiting cases of the finite-band ones. It is also indicated that there is an upper bound on the number of transmission zeros which may be introduced while maintaining the stability of the filter for a given degree. The technique represents the most comprehensive one available for the solution of the combined amplitude and phase approximation problem, and leads to a large family of stable transfer functions.

Synthesis of arbitrary digital transfer functions using allpass-based structures derived via LBR two-pair extraction procedure

The implementation of a digital filter transfer function with all transmission zeros on the unit circle is developed via the synthesis of an appropriate allpass function. The synthesis procedure is based on the “LBR-extraction” approach. The resulting structure is in the form of a doubly terminated cascade of lossless (LBR) two-pairs, with each two-pair realizing a single real or a pair of complex transmission zeros. The Concepts of complete and partial “1” removals, and “1” shifting are introduced and utilized during the synthesis process. The resulting structures have several properties in common with the Gray and Markel lattice filters, but do not require tap coefficients for numerator realization. The building blocks used in this paper are similar to those in certain wave-digital filters and orthogonal filters.

A new approach to the realization of low-sensitivity IIR digital filters

A new implementation of an IIR digital filter transfer function is presented that is structurally passive and, hence, has extremely low pass-band sensitivity. The structure is based on a simple parallel interconnection of two all-pass sections, with each section implemented in a structurally lossless manner. The structure shares a number of properties in common with wave lattice digital filters. Computer simulation results verifying the low-sensitivity feature are included, along with results on roundoff noise/dynamic range interaction. A large number of alternatives is available for the implementation of the all-pass sections, giving rise to the well-known wave lattice digital filters as a specific instance of the implementation.

Discrete version of Richard's theorem and applications to cascaded lattice realization of digital filter transfer matrices and functions

The well-known Richards' Theorem of the continuous-time filter theory is reformulated in the digital domain in a convenient manner, leading to a simple derivation of cascaded lattice digital filter structures, realizing lossless bounded transfer functions. The theorem is also extended to the matrix case, leading to a derivation of m -input p -output cascaded lattice filter structures with lossless building blocks, that realize an arbitrary p \times m digital Lossless Bounded Real (LBR) transfer matrix. Extensions to the synthesis of arbitrary, stable p \times m transfer matrices in the form of such cascaded lattices is also outlined. The derivation also places in evidence a means of testing the stability of an arbitrary p \times m transfer matrix of a discrete-time linear system.

Digital filter functions with short coefficients

A collection of highpass and bandpass digital-filter transfer functions is given. These all have short bit-length coefficients, allowing a very fast multiplication process. A general computational procedure for obtaining such functions is described.

On the design of digital filters as a sum of two all-pass filters

The necessary and sufficient conditions are given for a digital filter transfer function to be implementable as a sum of two all-pass filters. The conditions are derived directly in the z -plane. The class of filters satisfying these conditions is shown to be wider than the class of filters obtained via the bilinear transformation from the corresponding conventional analog filters. An example shows that the given conditions enable us to design complementary filter pairs with different numerator and denominator orders directly using magnitude squared functions. These filters compare favorably with the corresponding classical filters.