Group Delay Approximation Research Articles

Theoretical analysis and comparison of transient-extracting transform and time-reassigned synchrosqueezing transform

Transient-extracting transform (TET) and time-reassigned synchrosqueezing transform (TSST) developed under the framework of short-time Fourier transform (STFT) can effectively enhance the time–frequency (TF) resolution of nonstationary signal composed of multicomponent with impulse-like components. Nevertheless, the TET and TSST methods lack relevant theoretical support to ensure their practical application. In this paper, we supplement the theoretical analysis of these two methods and provide a new view to compare them. We first review the original definitions of TET and TSST proposed in the previous literatures. Then, we demonstrate the performance and properties of TSST and TET in detail, e.g., group delay (GD) approximation error, reconstruction error and boundary analysis, extraction principle of TET, and property derivation. Finally, the performance of TET and TSST is further compared in the analysis of the numerical and real signals. Through complete theoretical and property analysis, the application of TET and TSST in reality can be largely enhanced.

Formulas for orthogonal IIR wavelet filters

Explicit solutions are given for the rational function P(z) for two classes of IIR orthogonal two-band wavelet bases, for which the scaling filter is maximally flat. P(z) denotes the rational transfer function H(z)H(1/z), where H(z) is the (lowpass) scaling filter. The first is the class of solutions that are intermediate between the Daubechies (1992) and the Butterworth wavelets. It is found that the Daubechies, the Butterworth, and the intermediate solutions are unified by a single formula. The second is the class of scaling filters realizable as a parallel sum of two allpass filters (a particular case of which yields the class of symmetric IIR orthogonal wavelet bases). For this class, a closed-form solution is provided by the solution to an older problem in group delay approximation by digital allpole filters.

A technique for multiple criterion approximation of FIR filters in magnitude and group delay

In spite of the attention received by nonlinear phase (NLP) FIR filter design, the best way to solve this problem is still open to debate. The formulation of nonlinear phase FIR filter design in terms of simultaneous magnitude and group-delay approximation addresses the two parameters of ultimate interest for applications. The simultaneous minimization of these two functions (one of which, the group delay, rational) is approached on the basis of an original extension of the differential correction algorithm. The proposed design tool enjoys interesting theoretical properties and works very effectively. The filters obtained according to the multiple criterion optimization (MCO). Formulation are compared against filters that are optimal in the complex Chebychev norm. Then, the flexibility characteristic of MCO formulations of trading off between magnitude and group-delay performance is exemplified. >

An approximation method of group delay characteristics of 1‐D and 2‐D discrete time systems

AbstractIn the fields of signal transmission and its processing, compensation of phase or group delay distortion is an important problem.This paper proposes an approximation method of group delay characteristic of one‐dimensional (1‐D) and 2‐D discrete‐time systems using an extended equation error function as its performance index. Since the phase approximation problem is inherently nonlinear, some iterative approaches have been proposed. Its disadvantage is in the increase of the amount of computation.Another method to transform group delay approximation problem to power spectrum approximation problem is presented. This indirect approach leads to the minimum squared error problem which is easily solved but does not yield a satisfactory result.In the first part of this paper, the 1‐D group delay approximation problem is formulated to a linear problem in group delay domain. Then we apply the quasi‐least mean squared method to it. In the latter part of this paper, the 1‐D method is extended to the 2‐D group delay approximation problem. Some examples are shown to verify the effectiveness of the method.

Extended remez algorithms for filter amplitude and group delay approximation

Various Remez-type algorithms for the computation of rational filter functions of a general form are proposed. They allow filter amplitude and group delay functions to be arbitrarily shaped and tapered. Such functions can be applied to predistort for undesirable effects in communication systems such as sine (x), transmission line weighting or distortion due to nonideal components. High-order touch points are introduced as a generalisation of the concept of maximum flatness. They are used to trade off between the amplitude, group delay and passive sensitivity properties of a filter. The high-order touch points can be used directly to design a passive ladder prototype by an iterative algorithm.

A new approach to multicriterion optimization problem and its application to the design of 1-D digital filters

A novel method is presented for generating efficient points for the multicriterion optimization (MCO) problem. A novel function, the shifted minimax function, is defined that has the property that any efficient point of the MCO problem can be generated by minimizing the function with appropriately chosen shifts. Using this shifted minimax function for generating efficient points, the optimality conditions for the MCO problem have been derived. The method is also applied to the simultaneous amplitude and group delay approximation problem of 1-D digital filters. >

FIESTA-a filter educational synthesis teaching-aid

The authors describe a circuit synthesis program called FIESTA and its use is a teaching tool in both undergraduate and graduate courses. The program is very easy to use, is highly interactive, and contains graphics capabilities to give the student insights in active RC-filter design. FIESTA makes easier and faster the solution of the filter approximation problem, which traditionally involves use of tables and nomographs for a selected number of specifications. It is especially practical when a set of design specifications is not included in the tables. Highlights include Butterworth, Chebyshev, and Cauer approximations, and an arbitrary group-delay approximation. Circuit implementation is done using for illustration the Tow-Thomas biquadratic active RC-filter as the main basic block. Several computer exercises are suggested to complement classroom lectures and traditional 'paper and pencil design'. Addition of code is easy to implement in FIESTA. >

Constant group delay approximation via general Bessel-type polynomials

The use of the general Bessel-type polynomial for group delay approximation has been investigated and results described. The polynomials yield better results and are superior to those proposed by Johnson and Johnson.

Efficiently Realizable Digital Filter Transfer Functions

In this paper methods to design IIR digital filters with good attenuation or good attenuation and good group delay characteristics are described. These filters require often significantly less arithmetic operations than conventional efficient IIR and FIR digital filters. For the amplitude approximation problem the passband or stopband is mapped onto the whole unit circle where an equiripple behaviour is generated analytically. The desired stopband or passband behaviour is then obtained by locating the zeros or poles appropriately. For the simultaneous amplitude and group delay approximation problem the equiripple group delay of the all pole section of the filter is first generated on the whole unit circle and then mapped onto the passband. The linear phase FIR section of the filter makes the composite filter fulfill the amplitude specifications. Applications of the methods to some common filter design problems are presented.

Constant group delay approximation by series of Bessel polynomials

The transfer function obtained from the tuncated expansion of exp(p) in series of Bessel polynomials yield an approximation of the ideal filter. Thanks to a freely chosen parameter, it is possible to control the compromise between optimal amplitude and phase or between the rise time and the overshoot of the step response. Compared to the classical Thomson characteristic, which is linked to a single Bessel polynomial, the delay deviation in the passband is smaller.