Flat Group Delay Research Articles

A maximally flat group delay recursive digital filter with Chebyshev stopband attenuation

Due to the monotonically decaying nature of its magnitude response, an all-pole recursive digital filter, with its group delay approximating a prescribed constant value, does not exhibit a sharp transition band. Using transformation as the mathematical means, this correspondence describes a design technique for a recursive digital filter with a maximally flat group delay and a Chebyshev attenuation stopband.

Generalized bessel polynomials with application to the design of bandpass filters with approximately flat group delay response

AbstractThe continued fraction expansion of the ordinary Bessel polynomials is modified by replacing the complex frequency variable p by p/(1+γp), where γ=⩾0. The resulting polynomials, when a reactance transformation is applied, are capable of providing bandpass filters with an approximately flat group delay response.

Filters with Single Transmission Zeros at Real or Imaginary Frequencies

A new unified theory is presented for the synthesis of exactly equiripple low-pass prototypes having: a) one simple pole of attenuation at a real frequency; or b) a single pair of real-axis transmission zeros (giving linear-phase performance). These types of filters may be regarded as representing the least possible degree of complication over the conventional Chebyshev filter, and are usually realized with one extra cross coupling in the structure. It is demonstrated that this gives much improved skirt selectivity in the case of a finite frequency pole, making it a viable intermediate case between the Chebyshev and elliptic function filters, while in the case of real-frequency zeros, very flat group delay over 50 percent of the passband is achieved with minimal cost in insertion loss and skirt rejection. Approximate and exact synthesis techniques are described, including results for the previously neglected odd-degree case. Experimental results demonstrate agreement with theory.

Transfer Function of Maximally Flat Group Delay Low-Pass Filters with Equal-Ripple Attenuation in the Stopband and Flat Attenuation in the Passband

A general class of transfer functions of maximally flat group delay low-pass filters with equal-ripple attenuation in the stopband and flat attenuation in the passband is investigated. Filter transmission zeros are calculated and listed in a table.

Nonminimum-Phase Optimum-Amplitude Bandpass Waveguide Filters

The synthesis of narrow-bandpass waveguide filters having flat group delay and optimum-amplitude characteristics is described. The design utilizes either single- or dual-mode waveguide cavities. Experimental results for a 40-MHz-bandwidth filter centered at 4 GHz show excellent agreement with theory.

Recursive digital filters with maximally flat group delay

A well-known limitation of the recursive digital filter, when compared to the nonrecursive filter, is its incapability of having a strictly linear phase characteristic; thus it may only approximate a constant group delay. For the analog filters the choice of the maximally flat criterion leads to the use of the Bessel polynomials. Yet digital approximations of these continuous filter functions are inadequate to yield the true maximally flat delay approximation of the recursive filters. Our purpose is to provide for the problem at hand a solution obtained by a direct approximation procedure in the z plane. The denominator of the transfer function turns out to be a Gaussian hypergeometric function, more particularly connected with the Legendre functions. The stability of the filters is discussed and some numerical results in regard to the amplitude and phase responses as well as the pole loci are given.

Design of Chebyshev Filters with Flat Group-Delay Characteristics

In this paper, a method for designing Chebyshev filters having flat group-delay characteristics in the main part of the passband is presented. From the general approximation theory, a method for obtaining the transfer function of Chebyshev filters with complex transmission zeros is derived, which are so determined that the group-delay characteristics may be flat in the main part of the passband. A new theory of cascade synthesis, which is an extension of Belevitch's cycle, and an extended bisection theorem are introduced. By the applications of these results, Chebyshev filters with flat group delay can be realized. A practical design example is also included.

A Class of Transfer Functions Having Approximately Maximally Flat Group Delay Characteristics

A Class of Transfer Functions Having Approximately Maximally Flat Group Delay Characteristics