Design of zero-phase recursive 2-D variable filters with quadrantal symmetries

The digital filters with adjustable frequency-domain characteristics are called variable filters. Variable filters are useful in the applications where the filter characteristics are needed to be changeable during the course of signal processing. In such cases, if the existing traditional constant filter design techniques are applied to the design of new filters to satisfy the new desired characteristics when necessary, it will take a huge amount of design time. So it is desirable to have an efficient method which can fast obtain the new desired frequency-domain characteristics. Generally speaking, the frequency-domain characteristics of variable filters are determined by a set of spectral parameters such as cutoff frequency, transition bandwidth and passband width. Therefore, the characteristics of variable filters are the multi-dimensional (M-D) functions of such spectral parameters. This paper proposes an efficient technique which simplifies the difficult problem of designing a 2-D variable filter with quadrantally symmetric magnitude characteristics as the simple one that only needs the normal one-dimensional (1-D) constant digital filter designs and 1-D polynomial approximations. In applying such 2-D variable filters, only varying the part of 1-D polynomials can easily obtain new desired frequency-domain characteristics.     

Focusing resonance signatures in ultra-wideband SAR images byallpass filtering

This correspondence shows that resonance signatures in ultra-wideband synthetic aperture radar (SAR) images, which are smeared out due to their late arrival time, can be focused and extracted by postfiltering the SAR images with special two-dimensional (2-D) allpass filters. A design algorithm for FIR approximations to the desired allpass filters based on radial slice approximations (RSA) is presented.     

Variable digital filter design using the outer product expansion

Digital filters with adjustable frequency domain characteristics are referred to as variable digital filters. Variable filters are useful in the applications where the filter characteristics are required to be changeable during the course of signal processing. Especially in real time applications, variable filters are needed to change their coefficients instantaneously such that the real time signal processing can be performed. The present paper proposes a very efficient technique for variable 1D digital filter design. Generally speaking, the variable coefficients of variable digital filters are multidimensional functions of a set of spectral parameters which define the desired frequency domain characteristics. The authors first sample the given variable 1D magnitude specification and use the samples to construct a multidimensional array, then propose an outer product expansion method for expanding the multidimensional array as the sum of outer products of 1D arrays (vectors). Based on the outer product expansion, one can reduce the difficult problem of designing a variable 1D digital filter to the easy one that only needs constant 1D filter designs and 1D polynomial approximations. The technique can obtain variable 1D filters having arbitrary desired magnitude characteristics with a high design accuracy     

The acousto-optic effect in single-mode fiber tapers and couplers

All-fiber acousto-optic devices based on the null fused taper coupler have been successfully demonstrated as frequency shifters, variable splitters, switches and tunable filters. In this paper, the interaction upon which these devices are based has been extensively analyzed under a set of approximations that are valid in most cases. Simple analytical expressions for the important properties are derived, which provide a set of design rules for such devices     

Lowpass delay filters with flat magnitude and group delay constraints

This paper describes the design of finite impulse response (FIR) delay filters that minimize a squared error and have prescribed number of zeros at /spl omega/=/spl pi/ and prescribed magnitude and group delay flatness at /spl omega/=0. An important special case is the design of least squared error lowpass filters with prescribed flatness constraints and zeros at /spl omega/=/spl pi/. Even though the flatness constraints are in general nonlinear functions of the filter coefficients, we show the remarkable fact that for a subclass of the filters a simple orthogonal projection of least squared error filters onto a special linear subspace determined via Baher (1982) filters gives the solution. The paper also introduces the notion of delay filters that are high-order approximations to the ideal delay and establishes their equivalence to Baher filters. This connection gives novel elementary derivations of Baher filters and their properties. Matlab programs are provided at the end of the paper for the design of filters described in this paper.     

On the Elimination of Reactive Element Loops and the Use of Special Approximations in the Design of OTA-C Filters

Loops of reactive elements in passive filters cause a series of problems in OTA-C simulations of these structures. These loops can be eliminated in a systematic way by the procedures described in the paper. The use of special approximations in the design of the passive prototype filters allows the elimination of multiple loops of reactive elements that appear in usual LC ladder filters with finite transmission zeros. This leads to more efficient active simulations, where problems with floating capacitors, DC or high-frequency instability, or limited operating frequency are avoided.     

Approximation of 2-D analog and digital transfer functions using doubly terminated cascade-separable network properties

This paper considers certain useful approximations which can be obtained by doubly terminated two-variable cascade-separable networks. Since such networks can be transformed into 2-D wave digital filters, these approximations provide useful magnitude responses in the 2-D digital domain, also. Two approximation methods are discussed, and these can produce near quadrantal symmetry.     

Linear digital filtering for laboratory automation

The design of nonrecursive and recursive digital filters using linear least squares or linear minimum variance is described. This method of design requires a model, and since polynomial approximations are widely used in laboratory automation, a polynomial state model is first utilized. Then an exact scalar signal model is employed that results in a completely time-varying filter. For both models, the design leads to the recursive Kalman filter. The operation of the filters for noise reduction is first demonstrated for simulated data, and design forms are compared. For the exact scalar signal model, noise reduction and peak separation are demonstrated using simulated data and data obtained from a mass spectrometer. By using the correct model, excellent peak separation and noise reduction can be obtained.     

SVD-based design and new structures for variable fractional-delay digital filters

This paper shows that the problem of designing one-dimensional (1-D) variable fractional-delay (VFD) digital filter can be elegantly reduced to the easier subproblems that involve one-dimensional (1-D) constant filter (subfilter) designs and 1-D polynomial approximations. By utilizing the singular value decomposition (SVD) of the variable design specification, we prove that both 1-D constant filters and 1-D polynomials possess either symmetry or anti-symmetry simultaneously. Therefore, a VFD filter can be efficiently obtained by designing 1-D constant filters with symmetrical or antisymmetrical coefficients and performing 1-D symmetrical or antisymmetrical approximations. To perform the weighted-least-squares (WLS) VFD filter design, a new WLS-SVD method is also developed. Moreover, an objective criterion is proposed for selecting appropriate subfilter orders and polynomial degrees. Our computer simulations have shown that the SVD-based design and WLS-SVD design can achieve much higher design accuracy with significantly reduced filter, complexity than the existing WLS design method. Another important part of the paper proposes two new structures for efficiently implementing the resulting VFD filter, which require less computational complexity than the so-called Farrow structure.     

Design of General Manifold Multiplexers

The direct analytical design process for arbitrary multiplexers given in a previous paper is extended to the case of bandpass channel filters connected to a uniform-impedance manifold (e.g., a length of waveguide or transmission line). The previous approximations are greatly improved by adding immittance compensation in a way which not only preserves the canonic form of the network but also assists in the physical construction by spacing the filters along a manifold. The phase shifters between channels are themselves sufficient to compensate the filter interactions to such an extent that contiguous channeling cases are designable. The results are presented mainly in closed form requiring minimal computer optimization. Analysis of multiplexers with frequency-dependent manifolds indicate that there are restrictions on the total bandwidth, but a ten-channel multiplexer is probably feasible, suitable for input and output multiplexers required in typical communications systems. Practical results on a simple manifold triplexer are presented.     

B-spline design of maximally flat and prolate spheroidal-type FIRfilters

A digital FIR filter is described that offers excellent passband and stopband characteristics for general applications. Design formulae include parameters that adjust the magnitude response from one having characteristics like the maximally flat designs of Hermann (1971) and Kaiser (1975, 1979) to one having characteristics like the minimum-sidelobe energy approximations of Kaiser and Saramaki (1989). The impulse response coefficients are more straightforward to obtain than these filter designs while offering preferable response characteristics in many instances. Unlike FIR filters designed by window- or frequency-sampling methods, the filter coefficients are determined from the inverse Fourier transform in closed form once B-splines have been used to replace sharp transition edges of the magnitude response. Although the filters are developed in the frequency domain, a convergence window is identified in the convolution series and compared with windows of popular FIR filters. By means of example, adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs. The design technique is extended to create additional transitional filters from prototype window functions, such as the transitional Hann window filter. The filters are particularly suitable for precision filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but will also be useful in other applications requiring low passband and stopband errors     

Variable Digital Filter With Group Delay Flatness Specification or Phase Constraints

In this paper, we consider the design of finite-impulse response variable digital filters (VDFs) with variable cutoff frequency or variable fractional delay. We propose the design of VDFs with minimum integral squared error and constraints on the maximum error deviation in conjunction with flatness group delay specification or phase constraints. These specifications allow the VDFs to have approximately linear phase, especially in the passband. As these specifications are required to be satisfied for all the filters generated by the VDF with controllable spectral characteristics, the linear constraints resulting from the flatness specification are relaxed to inequality constraints. To make the optimization problem tractable for the phase constrained problem, suitable approximations are employed in the paper. The design problem is formulated as an optimization problem with a quadratic cost function and infinite number of constraints. A numerical scheme with adaptive grid step size is proposed for solving the optimization problem.     

Sharp Cutoff Microwave Filters

A class of sharp cutoff filters using combinations of lumped constant and distributed constant reactance have been analyzed and a test made of one type. The filters are developed in accordance with image parameter theory and are m-derived. Both high-pass and low-pass types are analyzed. The improvements over previous sharp-cutoff image parameter filters are predictable band limits and more predictable response. The derivations hold for all frequencies and are not approximations good only for short lengths of distributed constant reactance. Also, this class of filters have much sharper cutoffs than can be obtained with an equivalent number of sections designed using modern network theory. Some of these filters have fairly flat response close to the sharp-cutoff and are useful as end-matching sections. Curves and design equations are presented for three types---two high-pass and one low-pass filter. A seven-section high-pass filter was designed and tested. Its cutoff rate was 87db in a 3 per cent bandwidth located in the 300-Mc region. The pass-band width was greater than 30 per cent.     

Using a Genetic Algorithm to Optimize Capacitance Ratio Approximations in SC Filters

Accurate capacitance matching is one of the main design issues in switched-capacitor (SC) filters. Using identical unit capacitors in parallel to implement each filter capacitor, combined with a careful layout design, can provide an accuracy of 0.1% in the filter coefficients. The disadvantage of this technique is the fact that it can be directly applied only if the coefficients can be expressed as ratios of integer numbers. As a result, coefficient approximations are required, leading to frequency response errors. In this paper, a genetic algorithm (GA) is used to find the optimum capacitance ratio approximations by rational numbers that minimize the total number of unit capacitors for a given error tolerance in the frequency response. Design examples in 0.35 μm CMOS are presented and simulated to illustrate the proposed approach and verify its effectiveness.     

Design of arbitrary-phase variable digital filters using SVD-based vector-array decomposition

This paper proposes a straightforward method for designing variable digital filters with arbitrary variable magnitude as well as arbitrary fixed-phase or variable fractional delay (VFD) responses. The basic idea is to avoid the complicated direct design of one-dimensional (1-D) variable digital filters by decomposing the original variable filter design problem into easier subproblems that only require constant 1-D filter designs and multidimensional polynomial approximations. Through constant 1-D filter designs and multidimensional polynomial fits, we can easily obtain a variable digital filter satisfying the given variable design specifications. To decompose the original variable filter design into constant 1-D filter designs and multidimensional polynomial fits, a new multidimensional complex array decomposition called vector array decomposition (VAD) is proposed, which is based on two new theorems using the singular value decomposition (SVD). Once the VAD is obtained, the subproblems can be easily solved. Furthermore, we show that the VAD can also be generalized to the weighted least squares (WLS) case (WLS-VAD) for the WLS variable filter design. Three design examples are given to illustrate that the WLS-VAD and VAD-based techniques are considerably efficient for designing variable digital filters with arbitrary variable magnitude and arbitrary fixed-phase or VFD responses.     

Computational algorithm for the design of elliptic filters

A simple and fast algorithm, based on the simultaneous cheby?shev character of the passband and stopband characteristic, is presented for the computation of the transfer function of elliptic filters. The algorithm does not use elliptic functions; rather, a set of nonlinear equations is established and solved using Newton's method. Since useful initial approximations are easy to find, the solution requires only 2?4 iterations. The results are obtained directly in the transformed variable z and hence are immediately usable for computer-aided design.     

Slot-Line Field Components (Correspondence)

Formulas derived by mode summation give the six B- and H-field components in the various air and dielectric regions of a slot-line cross section. These formulas are valid except when very close to the slot, where approximations in the analysis cause a large error. A quasi-static method yields a second set of formulas that apply near the slot. Thus the field is determined satisfactorily in all parts of the cross section. Graphs of the H components show that elliptical polarization exists, with the best approach to circularity near the slot and near the opposite surface of the substrate. Quantitative field data are useful for analysis and design of slot-line components, such as ferrite devices, dielectric-resonator filters, directional couplers, and broad-band transitions to coaxial line or microstrip.     

Interdigital Band-Pass Filters

The design of band-pass filters using interdigital arrays of resonator line elements between parallel ground planes is discussed. Two approximate design procedures are described, both of which permit design directly from lumped element, low-pass, prototype filters. Both design procedures will work for either narrow or wide-band filters, but one procedure gives more practical dimensions for filters having wide bandwidths (such as an octave), while the other gives more practical dimensions for filters having narrow or moderate bandwidth. The resulting filters are very compact, have relatively noncritical manufacturing tolerances, and strong stop bands with the second pass band centered at three times the center frequency of the first pass band. The dimensions and measured performance curves are presented for a 10 per cent bandwidth design and an octave bandwidth design.