Digital Filter Transfer Function 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.

Group delay equalisation of discrete Butterworth tan filters in the continuous domain

ABSTRACTA new optimisation method for equalising the group delay frequency response of the discrete transfer function of recursive digital filters, so-called tan filters, is presented in this paper. The method is based on an algorithm that is used for a stable all-pass filter approximation. Allpass filter acts as a group delay equaliser, with the purpose of equalising group delay of the discrete tan filter in a maximal flat sense. The algorithm relies on a set of simultaneous nonlinear equations. These set equations are derived directly from the flatness conditions of the equalised group delay response at the origin in the analogue -domain, in order to obtain the unknown coefficient values of the discrete allpass filter. The iterative method most widely used for solving set nonlinear equations and Symbolic Math Toolbox for Matlab features for finding numerical solutions are presented in detail.In the given examples, firstly a discrete Butterworth tan filter was designed by using transfer function poles in closed form. Secondly, the Butterworth tan filter was augmented with cascade connection of non-minimum phase all-pass discrete filter, in order for the group delay response of the whole filter to be equalised in a maximally flat sense.

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.

Improving Efficiency of NPP Software Based I&C

The paper considers improving efficiency of NPP software based I&C during adjustment and readjustment of its characteristics. The research analyzes impact of transfer function coefficient of digital components on features of frequency-response characteristics, which shall be considered during design of software based I&C. The paper objective was to determine the numerator and denominator dependencies of transfer function of first order high-pass and low-pass digital filters of cut-off frequency, and also to determine dependencies on pulsation coefficient.

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.

Derivation of the Class of Digital Filters With All Second-Order Modes Equal

This paper reveals the class of digital filters with all second-order modes equal. We first prove that if the second-order modes of a digital filter are all equal, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -sensitivity minimization problem of the digital filter can be solved analytically. We derive a general expression of the transfer function of digital filters with all second-order modes equal. Furthermore, we show that the general expression is obtained by a frequency transformation on a first-order prototype FIR digital filter.

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.

Analysis of frequency-response sensitivity of the second-order sections with a redundant number of multipliers of recursive digital filters

The paper considers the possibilities for diminishing the sensitivity of frequency responses to variation of components’ parameters and the mean-square sensitivity of frequency responses of minimum-phase and nonminimum-phase sections with an excessive number of components. These sections are used for realization of transfer functions of recursive digital filters obtained at the approximation stage of design.

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>

Approximation of multivariable functions by M-D transfer functions with separable denominator

The approximation of a given function by a rational function has been considered extensively by mathematicians. A particular result has been stated by Walsh that the best approximation of a given analytical function is one which interpolates the given function at several properly chosen points. In this paper, transfer functions of multidimensional digital filters with separable denominator are used for the approximation of given multivariate functions. It is shown that the result of Walsh can be generalized in a straightforward manner. By an example it is illustrated how the new result can be applied to, e.g., the order reduction of a higher-order system. In the conclusion we state the usefulness and the limitation of the result.

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. >

The uniqueness in designing multidimensional causal recursive digital filters possessing magnitude hyperspherical symmetry

It is shown that magnitude hyperspherically symmetric transfer functions of multidimensional (MD) causal recursive digital filters must have numerator and denominator polynomials that are separately magnitude hyperspherically symmetric. Further, the exact reference-domain magnitude hyperspherically symmetric denominator polynomial is of infinite order, possessing only one free parameter, and the magnitude hyperspherically symmetric numerator polynomial itself has to be a radial even function. The corresponding MD design problem is shown to be essentially a one-dimensional design problem. Filter transfer functions having good symmetry and moderate degree can be designed by using the presented procedure. >

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.

The realization of linear shift-variant filters through state feedback

In this paper a new method to realize rational generalized transfer functions of linear shift-variant digital filters through state feedback is presented. In some practical applications the required characteristics of the filter change slowly. Under these circumstances, the proposed method is very effective and the resulting filter structure is simple. A numerical, example is provided to show the performance of the method.

The general solution of write equalization for RLL (d,k) codes

The author describes the collection of all possible transfer functions of digital recursive filters that, when operating at p times the original data rate on runlength-limited (RLL) (d,k) bipolar data, can transform each allowable input signal into a bipolar output signal. For all integer values of p, d, and k with p>or=1 and 0<or=d<k<or= infinity , the collection of all transfer functions of digital recursive filters that satisfy this constraint is determined. It is also shown that, even for small values of p and d, this collection contains many transfer functions that are not obtained by previously known methods.<<ETX>>

Narrow transition width two-dimensional digital fan filters with sum of powers-of-two coefficients

General expressions are presented for the transfer functions of quadrantal digital fan filters and 90° digital fan filters. Through a study of the coefficients of the transfer functions, a method for the design of multiplierless fan filters with sum of power-of-two lpar;SOPOT) coefficients using these formats is introduced and a table of SOPOT coefficients is given for filter order M ranging from 4 to 10, A number of examples have been tried.

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.