Selective Linear Phase Filters Research Articles

An approximation procedure for selective linear phase filters

A method is proposed for the simultaneous approximation of attenuation and group delay characteristics of analog and digital filters. The attenuation is approximated to be equal ripple in the passband and the stopband, while the group delay is equalized in the passband using a least-mean-square norm. The number of attenuation ripples in the passband, and the degrees of freedom for the group delay equalization can be traded off for the best possible approximation.

Selective linear-phase filters with controllable amplitude response

A method is presented for the construction of transfer functions of analog or digital filters exhibiting linear phase low-pass or bandpass characteristics. The group delay which is determined by the denominator polynomial can be maximally flat or equiripple in the whole or part of the passband. The passband loss as well as the stopband loss can be monotonic or have ripples with arbitrary widths. The iterative procedure involves the solutions to a polynomial and a set of linear equations.

Selective linear phase filters possessing a pair of J‐axis transmission zeros

AbstractA design technique is developed for prototype selective linear phase filters which have an equiripple passband amplitude response and a pair of j‐axis transmission zeros in the stopband while maintaining a linear phase characteristic in the passband. Since the basic technique requires numerical optimization techniques, the element values for several cases have been tabulated together with detailed response characteristics.One important result is that for certain characteristics, one internal cross‐coupling element may be designed to be zero. As a result, in the sixth degree case with only one extra cross‐coupling element between elements 1 and 6 a significant improvement in both the amplitude and group delay performance can be achieved as compared to the Chebyshev case. Owing to its importance, this case is investigated in detail and a 2.6 GHz post decoupled combline filter has been constructed based upon this prototype.

Selective constant delay filters with chebyshev passband amplitude response

AbstractThe aim of this letter is to show that the principle of least squares norm can be utilized to offer flexibility in the design of selective linear phase filters.

Design of selective linear-phase filters with equiripple amplitude characteristics

A simple numerical technique is described for the construction of a nonminimum phase transfer function with an optimum equiripple passband amplitude response and linear-phase characteristics. The linearphase behavior may be maintained over part of or over the entire passband by varying the number of transmission zeros at infinity. Increasing the number increases the selectivity of the filter at the expense of a deterioration in the phase performance towards the edge of the passband. Synthesis is performed using even- and odd-mode decomposition, and tables of element values are provided with graphical design information to enable the design engineer to choose the correct prototype to meet a given specification.

In-Line Waveguide Selective Linear Phase Filters

A procedure is described whereby narrow-band waveguide selective linear phase filters may be designed from a low-pass prototype linear phase network. The structure is comprised of a cascade connection of basic sections, each containing a direct-coupled cavity together with a dual-mode resonator. Each dual-mode resonator takes the form of a square guide mounted on the broad wall of the main rectangular guide and coupled to this guide by a small aperture. Explicit formulas for the susceptance of the coupling apertures and electrical lengths of the cavities are given in terms of the low-pass prototype.

Cascade Synthesis of Selective Linear-Phase Filters

A design procedure is presented for the realization of selective linear-phase channel filters in a cascade configuration. From the transfer function which exhibits optimum maximally fiat amplitude and linear phase characteristics, synthesis is performed using symmetrical seconddegree transmission zero producing sections which contain frequencyinvariant reactances, and the overall network is constructed with complex conjugate symmetry. Conversion is made to lumped-element bandpass channel filters using the reactance slope parameter method. In all but very narrow bandwidths, dispersion occurs in the bandpass filter, but it is shown that by choosing a dispersive modification to the prototype, flat group-delay characteristics may be recovered in the bandpass filter.

A Low-Pass Prototype Network for Microwave Linear Phase Filters

A new approximation theory is presented for a low-pass prototype filter which simultaneously optimizes both the passband amplitude and phase response of the scattering transfer coefficient over the same finite band. This closed form solution is expressed in terms of single polynomial, which is readily generated through a simple recurrence formula, and has been termed the equidistant linear phase polynomial since its phase deviation from linearity vanishes at equidistant points along the real frequency axis. A synthesis procedure is presented for the realization of this transfer function using a resistively terminated, symmetrical, lossless, two-port network where extensive use is made of the immittance inverter concept. The even-mode admittance, which defines the network, possesses a simple closed form representation in terms of the equidistant linear phase polynomial and its derivative, and consequently, the entire theory is derived in an analytic form. Typical performance characteristics are graphically presented for networks of up to 14th degree, illustrating the superiority of this new approach over any other known form of approximation theory for selective linear phase filters.