Generalised class of nonlinear-type hybrid filters

A new class of nonlinear filters called the generalised directional distance rational hybrid filters (GDDRHF) for multidimensional signal processing is described. The application at hand is colour image filtering problems. The GDDRHF filter is a two-stage filter, which exploits the features of a new directional distance filter, where the temporal information related to the central sample is expressed by its weight, and those of the rational operator. This weight is incorporated to a sum of vector distances and vector angles. It is shown that the new GDDRHF outperforms a number of widely known nonlinear filters with respect to all criteria used.     

Generalised Cheby?shev lowpass filters

An expression is presented from which the pole positions of any shifted Cheby?shev lowpass filter can be evaluated. The standard Cheby?shev filters are shown to be special cases.     

Sensitivity formulas for digital lattice filters

Formulas are given for the sensitivities of the transfer function with respect to the k-parameters in a digital lattice structure.     

Adaptive lattice filters for CDMA overlay

This paper presents the behavior of reflection coefficients of a stochastic gradient lattice (SGL) filter applied to a code division multiple-access overlay system. Analytic expressions for coefficients for a two-stage filter are derived in a Rayleigh fading channel with the presence of narrow-band interference and additive white Gaussian noise. It is shown that the coefficients of the lattice filter exhibit separate tracking and convergent properties, and that compared to an LMS filter, the lattice filter provides fast rate of convergence, while having good capability of narrow-hand interference suppression     

Adaptive lattice bilinear filters

Two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models are presented. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem, thus using multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs. This method is conceptually very simple, but results in biased system models in the presence of measurement noise. The second is an approximate least-squares output error solution; the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method     

Non-symmetric lattice structure for pole zero filters

This communication generalizes the lattice structure of IIR digital filters and shows its relation with classical structures. The algorithm for computing the corresponding reflection coefficients is given. It is also shown that this algorithm computes the greatest common divisor of the numerator and the denominator of the transfer function.     

One-multiplier adaptive lattice algorithm for recursive filters

The formulation of one-multiplier lattice structures of the Gray-Markel type forinfinite impulse response filters is reviewed. Several special cases of this formulation — including the well-known Gray-Markel normalized lattice—are presented as scaled polynomial versions of the two-multiplier lattice. A new adaptive algorithm is presented for updating the parameters of one-multiplier lattice structured recursive filters. The LMS-based algorithm requires fewer computations than earlier reported algorithms [1]–[4].The research reported here was conducted with funds administered by the Naval Postgraduate School research council.     

Lightwave lattice filters for optically multiplexed communicationsystems

It has proven desirable to use multistage etalons and resonators in lightwave communication systems. The design of these linear structures, however, is made difficult by the manner in which their transfer functions are nonlinear with respect to their composite reflection coefficients. If we interpret the etalons as discrete-time lattice filters, then z-transform techniques may be used to recursively synthesize filters with desirable properties. An algorithm is developed which can be used to design the arbitrary all-pole transfer functions in transmission, and the restricted class of pole-zero transfer functions in reflection, which are possible to implement with this architecture. We present some design examples such as notch, or channel-blocking, filters and flat-top bandpass, or channel-passing, filters which are appropriate for frequency-division multiple access and wavelength-division multiplexed communications systems. The theory predicts, and we show experimentally, how these structures may be used to discriminate, or route, signals based on their modulated or coded characteristics     

Equivalent network for bridged crystal filters

An equivalent circuit for a capacitively bridged coupled resonator is described. Bridged T networks may be obtained from ladder networks by using this transformation.     

Lowpass-bandpass transformation for active RC filters

The conventional lowpass-bandpass transformation (transformation of each element separately) is not applicable to active RC networks because it leads to networks also containing inductors. A modified transformation, including explicit design formulas, will be described, which is applicable to the design of active RC bandpass filters realised by cascading 2nd-order sections.     

Extended RLS lattice adaptive filters

This paper solves the problem of developing exact fast weighted RLS lattice adaptive filters for input signals induced by general orthonormal filter models. The resulting algorithm can be viewed as a counterpart of the extended fast fixed-order RLS adaptive filters previously derived.     

Cascade lattice IIR adaptive filters

The feedback lattice filter forms, including the two-multiplier form and the normalized form, are examined with respect to their relationships to the feedback direct form filter. Specifically, the transformation matrix between the lattice forms and the direct form is derived; parameter and state relationships between the lattice forms and the direct form are therefore obtained. An IIR filter structure-the cascade lattice IIR structure-is constructed. Based on this structure, three IIR adaptive filtering algorithms in the two-multiplier form can then be developed following the gradient approach, the Steiglitz-McBride approach and the hyperstability approach. Convergence of these algorithms is theoretically analyzed using either the ODE approach or the hyperstability theorem. These algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms. Relationships of the simplified algorithms to the direct form algorithms are also studied, which disclose a consistency in algorithm structure regardless of the filter form. Three normalized lattice algorithms can also be derived from the two-multiplier lattice algorithms. Experimental results show much improved performance of the normalized lattice algorithms over the two-multiplier lattice algorithms and the direct form algorithms     

Convergence of adaptive lattice filters

Some results are presented on the convergence rate of lattice filters when adaptive algorithms are employed for estimating their reflection coefficients. It is shown that, unlike tapped-delay-line filters, adaptive lattices are not affected by ill-conditioned data.     

Computable real lattice structures for cochlea-like digital filters

A synthesis algorithm for a pipelined lattice implementation of cochlea-like digital filters is presented, based upon the properties of real, lossless lattice synthesis of ARMA filters. The algorithm operates on a simplified characterization of elementary lattice sections of degree one or degree two. This leads to a structure that is recursively designed and for which each lattice is precisely implemented by a pair of complex conjugate transmission zeros via Richard's function extractions. Except for zeros of transmission on the unit circle, all other types and multiplicities are allowed. Necessary and sufficient conditions are derived for the degree-two lattices to guarantee computability, i.e., realizability with no delay-free loops. In addition to being suitable for VLSI realization, the structure enables a systematic cochlea assessment from the scattering ear parameters.     

New adaptive normalised lattice algorithm for recursive filters

A new adaptive algorithm is presented for updating the parameters of normalised lattice structured recursive filters. The normalised lattice can be represented in the form of CORDIC blocks by converting the reflection factors into trigonometric functions. The LMS based algorithm actually updates the arguments of these trigonometric functions, and requires fewer computations than an earlier reported algorithm     

Simple design procedure for single-sideband crystal filters

The letter gives simple, direct formulas for the design single-sideband crystal `ladder? filters. The resulting designs are easily realisable by using only crystals and capacitors.     

Sinh-Domain linear transformation filters

A new systematic method for designing Sinh-Domain linear transformation (LT) filters is introduced in this article. For this purpose, a substitution scheme containing the Sinh-Domain LT equivalent of each passive prototype has been introduced. The proposed equivalents have been realised by employing appropriate Sinh-Domain building blocks with low-voltage operation capability. As an example, a third-order Sinh-Domain elliptic LT filter has been designed and its performance has been evaluated through simulation results. In addition, a detailed comparison with the corresponding Sinh-Domain and log-domain counterparts has been performed and the obtained results have been further discussed.     

Systolic architectures for adaptive multichannel least squares lattice filters

A family of systolic array architectures for adaptive multichannel least squares lattice (MLSL) filters is presented. These architectures are based on a recently developed algorithm that provides an efficient, numerically sound, and well-structured set of recursions for realizing MLSL filters. The algorithm is based on the recursive QR decomposition of the forward and backward error correlation matrices. Form input channels andp filter taps,O(pm ²) computations are required per time step. Numerous space-time tradeoffs are available in mapping the algorithm's recursions to systolic architectures, leading to the architectural family presented here.Los Alamos National Laboratory is operated by the University of California for the United States Department of Energy under contract W-7405-ENG-36.     

A lattice realization for 2-D separable-denominator digital filters

New properties useful in connection with 1-D and 2-D lattice realizations are developed. These properties enable one to represent given, complicated 2-D separable-denominator digital filters in terms of simpler, more elemental building blocks which consist of two 1-D lattice realizations having dynamics in different directions and connected in a cascade form. The matrix-relationship between a 2-D discrete Schwarz form and a controller-observer canonical form is also derived. A notable property of the proposed 2-D lattice realization is that the impulse response energy of a 2-D separable-denominator digital filter can be readily obtained from the reflection coefficients and input/output tapped coefficients of the realization.This work was supported by the National Science Council of the Republic of China under Grant NSC79-0402-E0006-02, the US Army Research Office under Grant DAAL-03-91-G0106, and the NASA-Johnson Space Center under Grant NAG-9-380.