Synthesis Of Recursive Digital Filters Research Articles

Synthesis of Recursive Digital Filters with Finite Word Length: Problems and their Solutions

Synthesis of Recursive Digital Filters with Finite Word Length: Problems and their Solutions

Синтез рекурсивных цифровых фильтров с конечной длиной слова: проблемы и их решения

Синтез рекурсивных цифровых фильтров с конечной длиной слова: проблемы и их решения

Transitional Butter–Elliptic filter suitable for complementary decomposition

Direct synthesis of recursive digital filters, whose characteristic function belongs to the new IIR filters class, is described in this article. Attenuation characteristic in the passband lies between the Butterworth's and the Elliptic's attenuation characteristics. All zeros of transfer function are placed on the unit circle so that the condition for complementary decomposition is fulfilled. Complementary decomposition into parallel connection of two allpass filters is performed. Then, lowpass filter is obtained summing these two filters and its complementary highpass filter – by their subtraction. The main advantage of this kind of filters is its smaller sensitivity to digital word length change compared to standard filters.

A novel approach to the synthesis of recursive digital filters with linear phase

The synthesis of recursive digital filters with linear phase is approached by means of existing approximation techniques. The design is based on a finite impulse response (FIR) filter that represents the ideal filter in terms of both magnitude and phase characteristics. The recursive digital filter with linear phase is then synthesized as an approximation of the FIR model where optimal Hankel approximation theory as well as the model reduction techniques are used. The causality and stability of the designed filter are guaranteed. This technique is used for designing both one-dimensional and two-dimensional recursive digital filters with linear phase, and is illustrated by a few numerical examples. >

Synthesis of recursive digital filters by state feedback of non‐recursive cascaded lattice filters

AbstractA general method to realize any digital transfer function is presented. The method is understood as a two‐stage process. First, a non‐recursive system having the same transfer zeros as the given transfer function is synthesized in the form of a special cascaded lattice structure. Then the poles of the non‐recursive system, which occur exclusively at the origin, are shifted by extending this system through state feedback so that the shifted poles coincide with the poles of the specified transfer function while the transfer zeros remain unchanged.1 Compared with the well‐known cascaded lattice structures proposed by Mitra et al.2 the resulting filters exhibit advantages in the realization of the adders. Furthermore, it is pointed out how the cascaded lattice structure2 can be derived from the structure introduced here by applying a state transformation.

Synthesis of recursive digital filters with prescribed attenuation and group-delay characteristics

A method of synthesizing recursive digital filters with pre- where scribed attenuation and group-delay characteristics is presented. The method depends on the fact that the introduction of complex transmission zeros into the transfer function of the filter network allows independent control of both attenuation and group-delay responses of the filter. An example is presented which clearly demonstrates the improvement in attenuation response obtained when complex transmission zeros are introduced into the transfer function of the filter.

Synthesis of recursive digital filters

The coefficients of a parallel programmed recursive digital filter are obtained using the nonlinear optimization algorithms described by Fletcher and Powell and Fletcher and Reeves. The technique is based on least square error criterion. The strategy adopted is the same as that of Steiglitz. The flowchart is given and the frequency responses for this filter obtained from the optimized values are compared. The Fletcher and Powell algorithm is found to give better results.

Considerations of the Padé approximant technique in the synthesis of recursive digital filters

The Padé approximant technique provides a quick design of recursive digital filters. An added advantage of the technique lies in that spectrum shaping requirements as well as linear phase constraints can be handled easily, even for higher order filters. This is important in supplying initial guesses of the filter parameters to iterative routines that would then seek a locally optimal design solution. These advantages are among those discussed in a partly tutorial presentation of the technique that relates to filter needs found in data transmission systems. In addition, the question of stability is treated and a new criterion is presented. The criterion provides sufficient conditions in establishing stability for a filter designed by using the Padé approximant technique.

Time-domain synthesis of recursive digital filters†

The synthesis of infinite memory digital filters for the operations of smoothing, filtering, prediction and differentiation is described. In the design, constraints are developed using a polynomial approximation to the signal. The noise is then minimized subject to the constraints using the method of Lagrangian multipliers.

Optimal least squares time-domain synthesis of recursive digital filters

A method for finding the coefficients of an nth-order linear recursive digital filter, which gives the best least squares approximation to a desired pulse response over a finite interval, is presented. A relationship is derived between the approximating error corresponding to an optimal set of numerator coefficients and the error produced by an overdetermined set of linear equations, which is a function of the denominator coefficients only. This relation provides a computational algorithm for calculating the optimal coefficients by iteratively solving weighted sets of linear equations in terms of the denominator coefficients only. Both theoretical and numerical results are presented. Also, bounds are found on the interval in which the norm of the optimum error must lie.

Time domain design of recursive digital filters

The problem of synthesis of recursive digital filters to give a desired pulse response over a specified interval is studied. Realizability conditions are stated and a linear design method is developed. Several design procedures that require only linear calculations are given for approximate realization of recursive filters. Finally, an error analysis of the techniques is made.

Synthesis of recursive digital filters using the FFT

It has been shown that recursive digital filters can be synthesized using the fast Fourier transform. An algorithm for computer implementation has been developed and used in comparing the computation times and noise figures of filters synthesized in this manner with the computation times and noise figures of filters synthesized by recursion. A model has been proposed for analysis of noise in the two-pole filter. Predictions of this model have been found to be in good agreement with noise measurements.

The Synthesis of Recursive Digital Filters

The circumstances and methods of the synthesis of linear digital recursive filters which are both stable and physically realizable are described. It is shown that any amplitude requency transfer function expressible as an even trigonometric rational polynomial can be synthesized by a real stable linear digital recursive filter. The degree of the corresponding difference equation is twice the degree of the denominator of the rational trigonometric polynomial. A class of even rational trigonometric functions which exhibit pointwise convergence to the deal rectangular low or high-pass amplitude frequency transfer function is chosen. A member of this class is shown to approximate more closely the ideal rectangular filter than does the corresponding classical continuous Butterworth filter. This class of filters is then mechanized. The phase and unit-impulse response functions are calculated for the corresponding difference equations of degrees 2 and 4.