Waveguide Bandstop Elliptic Function Filters

Using the "natural prototype" for elliptic function filters, a design procedure is presented for a class of waveguide bandstop filters, which exhibit equiripple passband and stopband responses. Due to the availability of explicit formulas for element values in the natural prototype elliptic function filter, the design procedure is entirely analytic and does not require numerical synthesis techniques. The resulting physical structure is the familiar uniform guide with iris-coupled series stubs. Unlike the bandstop filters designed from maximally flat or Chebyshev prototypes, the elliptic function design results in stubs that are not exactly three-quarter-wave coupled.     

Generalized Interdigital Linear Phase Filter

The design theory is presented for narrow-band generalized interdigital linear phase filters which consist of a pair of identical cross-coupled interdigital lines. The procedure for the determination of the characteristic admittances of the elements which describe the structure based upon the element values of the low-pass linear phase prototype network is given, from which the physical dimensions of the filter may readily be obtained. The measured performance characteristics of two filters are presented. The first is a 2.5 percent bandwidth 14-element filter based upon the maximally flat prototype operating in L-band, and the second is a 1 percent bandwidth 18-element version based upon the finite band prototype in S-band. Both filters are shown to be in excellent agreement with theory, with the latter exhibiting transfer characteristics considerably superior to those obtainable from any form of conventionally equalized filter of similar overall degree.     

Universal maximally flat lowpass FIR systems

The family of FIR digital filters with maximally flat magnitude and group delay response is considered. The filters were proposed by Baher (1982), who furnished them with an analytic procedure for derivation of their transfer function. The contributions of this paper are the following. A simplified formula is presented for the transfer function of the filters. The equivalence of the novel formula with a formula that is derived from Baher's analytical procedure is proved using a modern method for automatic proof of identities involving binomial coefficients. The universality of Baher's filters is then established by proving that they include linear-phase filters, generalized half-band filters, and fractional delay systems. In this way, several classes of maximally flat filters are unified under a single formula. The generating function of the filters is also derived. This enables us to develop multiplierless cellular array structures for exact realization of a subset of the filters. The subset that enjoys such multiplierless realizations includes linear-phase filters, some nonsymmetric filters, and generalized halfband filters. A procedure for designing the cellular array structures is also presented     

A technique for realizing linear phase IIR filters

A real-time IIR filter structure is presented that possesses exact phase linearity with 10~1000 times fewer general multiplies than conventional FIR filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay IIR filters. This structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real-time recursive implementation of the noncausal transfer function H(z^-1). The time reversed section technique used to realize exactly linear phase IIR filters is described. The effects of finite section length on the sectional convolution are analyzed. A simulation methodology is developed to address the special requirements of simulating a time reversed section filter. A design example is presented, with computer simulation to illustrate performance, in terms of overall magnitude response and phase linearity, as a function of finite section length. Nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct FIR implementation     

Frequency and time domain comparison of selective polynomial filters with corrected phase characteristics

Two solutions to the polynomial filter’s transfer function synthesis problem are considered for comparison in the frequency and time domain: the broad class of filters with a critical monotonic amplitude characteristic (CMAC) in the passband and filters which use Chebyshev (C) polynomials. To complete the synthesis procedure for linear phase applications, group delay correctors are considered, for which a convenient approximation procedure is proposed here. Comparisons of the original functions and the corrected ones are performed in the frequency and time domain. It is shown that when CMAC and C are compared as such, the latter is by no means preferable from the selectivity point of view, while the opposite stands when the comparison is based on passband amplitude distortions. When phase-corrected filtering functions are compared, based on circuit complexity and time domain performance, the CMAC are shown to be preferable.     

A new class of two-channel biorthogonal filter banks and waveletbases

Proposes a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters     

A new class of orthonormal symmetric wavelet bases using a complexallpass filter

This paper considers the design of the whole sample symmetric (WSS) paraunitary filterbanks composed of a single complex allpass filter and gives a new class of real-valued orthonormal symmetric wavelet bases. First, the conditions that the complex allpass filter has to satisfy are derived from the symmetry and orthonormality conditions of wavelets, and its transfer function is given to satisfy these conditions. Second, the paraunitary filter banks are designed by using the derived transfer function from the viewpoints of the regularity and frequency selectivity. A new method for designing the proposed paraunitary filterbanks with a given degrees of flatness is presented. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez exchange algorithm. Therefore, the filter coefficients can be easily obtained by solving the eigenvalue problem, and the optimal solution is attained through a few iterations. Furthermore, both the maximally flat and minimax solutions are also included in the proposed method as two specific cases. The maximally flat filters have a closed-form solution without any iteration. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method     

An alternative simultaneous maximally flat approximation for a low-pass recursive digital filter

Digital filters with either maximally flat magnitude or maximally flat group delay are known [1]-[3]. This paper offers an approach to the design of a recursive digital filter with simultaneous approximation to both magnitude and phase. Although the same Taylor norm is used, this described technique is different from the previous approach [4] in the sense that it employs a power series expansion around ω = 0 in the z-plane. It gives an alternative insight into the problem for the designers who are more familiar with the z-plane than the Richards' λ-plane. The filter transfer functions are obtained explicitly in closed forms.     

Wavelet Packets Analysis Based on IIR Two-channel Bi-orthogonal Filter Banks

1IntroductionAccordingtoitSrelationwithwaveletanalysis,tWo-channelfilterbankscanbeusednotonlyintheimplementationofwavelettransformandinversetransform,butalsoinwavelet'sconsmichon.AndIIRfiltersarewellknowntohaveshadertransihonregions,lowcomplexity,lowreconstrUctionermrandaPPro~lylinearphase.Weconstr'UctIIRhi-orthogonalPerfectreconstructionfilterbanksusinganallpassfunchonA(z)whoseamplitUdecharacterishcsisallpassandwhosephasecharacterishcsisanapproximatelylinearPhaseinthepass-band.Andweacc…     

Closed-Form Design of Half-Sample Delay IIR Filter Using Continued Fraction Expansion

In this paper, the closed-form design of half-sample delay infinite-impulse response (IIR) filter is presented. First, the continued fraction expansion (CFE) and its recursive computation are reviewed briefly. Then, the CFE of square root function is applied to design half-sample delay IIR filters with various orders. The comparisons with conventional maximally flat half-sample delay all-pass and Lagrange filters are made and implementation issue is also addressed. Next, the designed half-sample delay filter is used to reduce the approximation error of the conventional IIR Simpson integrator, to design half-band and diamond shaped filters, and to magnify the digital image. Finally, several numerical examples are illustrated to demonstrate the effectiveness of the proposed design method     

Explicit formula for the coefficients of maximally flat nonrecursive digital filter transfer functions expressed in powers of cos w

An explicit formula for the coefficients of the transfer function of a maximally flat nonrecursive digital filter, expressed in powers of cos w, is derived by exploiting the properties of the Kaiser-Hamming [1] amplitude change function polynomial. Transfer functions expressed in this form are convenient for implementing variable cutoff filters [2].     

Active RC nonminimum phase network using the DVCCS/DVCVS

A new configuration for realizing a second-order nonminimum phase transfer function using the differential voltage controlled current source, differential voltage controlled voltage source (DVCCS/ DVCVS) as the active building block is given. The special cases of a notch filter and an all-pass network are considered. Recently [1], the DVCCS/DVCVS [2]-[3] was used as the active building block in the realization of bandpass and lowpass filters. In this letter the synthesis of a second-order nonminimum phase transfer function using the DVCCS/DVCVS is considered.     

Direct Coupled Coaxial and Waveguide Band-Pass Filters (Correspondence)

In this note, experimental results will be presented for practical coaxial and waveguide band-pass filters. Filters of both types were originally developed in the 1700 Mc to 2300 Mc frequency range for application in a wide-band microwave radio relay communications system. The specifications for these filters called for very low input VSWR's over an appreciable part of the filter pass bands. This is necessary to minimize the degradation in system performance due to intermodulation noise resulting from feeder distortion of microwave transmission lines and/or group delay distortion within the microwave filters. Both the coaxial and waveguide band-pass filters employed five direct coupled resonators. Filters were designed for Butterworth (maximally flat amplitude) response shapes and nominal filter 3 db bandwidths of 60 Mc     

Two-Channel FIR Filter Banks Utilizing the FRM Approach

The frequency-response masking (FRM) approach has been introduced as a means of generating narrow transition band linear-phase finite impulse response (FIR) filters with a low arithmetic complexity. This paper proposes an approach for synthesizing two-channel maximally decimated FIR filter banks utilizing the FRM technique. For this purpose, a new class of FRM filters is introduced. Filters belonging to this class are used for synthesizing nonlinear-phase analysis and synthesis filters for two types of two-channel filter banks. For the first type, there exist no phase distortion and aliasing errors, but this type suffers from a small amplitude distortion as for the well-known quadrature mirror filter (QMF) banks. Compared to conventional QMF filter banks, the proposed banks lower significantly the overall arithmetic complexity at the expense of a somewhat increased overall filter bank delay in applications demanding narrow transition bands. For the second type, there are also small aliasing errors, allowing one to reduce the arithmetic complexity even further. Efficient structures are introduced for implementing the proposed filter banks, and algorithms are described for maximizing the stopband attenuations of the analysis and synthesis filters in the minimax sense subject to the given allowable amplitude and/or aliasing errors. Examples are included illustrating the benefits provided by the proposed filter banks.     

A Class of Minimum-Phase Microwave Filters with Simultaneous Conditions on Amplitude and Delay

The class of filters considered here is such that with a prescribed numerator for the transducer power gain (a constant or (1/spl lambda//sup 2/)/sup r/) the available degrees of freedom are divided to provide some zero derivatives of delay and some zero derivatives of the amplitude response at the origin. This enables one to progress in a smooth fashion from the maximally flat amplitude response to the maximally flat delay response. The results are derived by starting from the key case where the numbers of zero derivatives in amplitude and delay are equal. Results are presented for all-stub, cascaded transmission line, and interdigital realizations, and it is indicated how the technique may be applied for any prescribed even numerator in the transducer power gain. The results obtained indicate that this class of functions is particularly suitable for relatively wide passbands.     

Dispersive properties of optical filters for WDM systems

Wavelength division multiplexing (WDM) communication systems invariably require good optical filters meeting stringent requirements on their amplitude response, the ideal being a perfectly rectangular filter. To achieve high bandwidth utilization, the phase response of these filters is of equal importance, with the ideal filter having perfectly linear phase and therefore constant time delay and no dispersion. This aspect of optical filters for WDM systems has not received much attention until very recently. It is the objective of this paper to consider the phase response and resulting dispersion of optical filters in general and their impact on WDM system performance. To this end we use general concepts from linear systems, in particular, minimum and nonminimum phase response and the applicability of Hilbert transforms (also known as Kramers-Kronig relations). We analyze three different classes of optical filters, which are currently being used in WDM systems and compare their performance in terms of their phase response. Finally, we consider possible ways of linearizing the phase response without affecting the amplitude response, in an attempt to approximate the ideal filter and achieve the highest bandwidth utilization     

An Applied Method for Designing Maximally Decimating Non-uniform Filter Banks

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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.     

The Stepped Digital Elliptic Filter

The design and synthesis of various types of microwave elliptic function filters has been accomplished by a number of authors. However, one problem in this field which remains is the realization of compact narrow-band bandpass elliptic function filters. In this paper, a procedure is presented which enables this class of filters to be constricted in a compact digital form. Since the physical realization is in the form of an n-wire line, one-quarter of a wavelength Iong at the center frequency of the passband, where the impedance levels are stepped along the center of the coupled lines, the filter has been termed the stepped digital elliptic filter. The absence of awkward interconnections in the filter due to the stepped digital structure inherently implies that reasonable insertion loss characteristics may be achieved in the X-band region and above, and also simplifies the mechanical construction. It is shown that the resonant elements in the filter, due to the design procedure adopted, are relatively insensitive to the absolute bandwidth of the filter, and consequently fractional bandwidths of approximately 30 percent and below may be readily achieved while the normalized impedance values of the elements in the network remain of the order of unity. This latter result is similar to that obtainable from conventional interdigital filters but in the case of narrow bandwidths the stepped digital filter is considerably smaller in physical size. A systematic procedure is also formulated for the inclusion of the parasitic lumped end effect capacitances into the overall design procedure in order to maintain the equiripple passband and stopband responses. Experimental results are presented for a five-element, 11 percent bandwidth filter and are shown to be in good agreement with theoretical predictions.