Lattice Digital Filters Research Articles

Convergence models for lattice joint process estimators and least squares algorithms

A simple model characterizing the convergence properties of an adaptive digital lattice filter using gradient algorithms has been reported [1]. This model is extended to the least mean square (LMS) lattice joint process estimator [5], and to the least squares (LS) lattice and "fast" Kalman algorithms [9] -[16]. The models in each case are compared with computer simulation. The single-stage LMS lattice analysis presented in [1] is also applied to the LS lattice. Results indicate that for stationary inputs, the LMS lattice and LS algorithms exhibit similar behavior.

Lattice recursive digital filters

A method is proposed for synthesizing a recursive digital filter based on the lattice scheme. The resulting new structure has consequently the optimal properties of the lattice. In particular, the low sensitivity with respect to multiplier coefficients is illustrated by an example.

Synthesis of lattice digital filters by the state variable method

AbstractOne method for realizing a rational transfer function as a lattice digital filter is the procedure of Gray et al. using tap coefficient devices. Use of these devices should be avoided from the viewpoint of minimizing the number of multipliers. We have derived a discrimination condition and divided the structures into two classes; those realizing the rational transfer functions with lattice structures only and those requiring tap coefficient structures. A method is proposed for constructing lattice digital filters based on the state‐variable procedure. This method is systematic and suited for computer‐based design. The analysis is also simple. In the case of a general nth order filter it is shown that the coefficient sensitivity is low and a zero‐input limit cycle never occurs in complement truncation.

Convergence properties of an adaptive digital lattice filter

Convergence properties of a continuously adaptive digital lattice filter used as a linear predictor are investigated for both an unnormalized and a normalized gradient adaptation algorithm. The PARCOR coefficient mean values and the output mean-square error (MSE) are approximated and a simple model is described which approximates these quantities as functions of time. Calculated curves using this model are compared with simulation results. Results obtained for a two-stage lattice are then compared with the two-stage least mean-square (LMS) transversal filter algorithm, demonstrating that it is possible but unlikely for the transversal filter to converge faster than the analogous lattice filter.

Convergence properties of an adaptive digital lattice filter

Convergence properties of a continuously adaptive digital lattice filter used as a linear predictor are investigated for both an unnormalized and a normalized gradient adaptation algorithm. The PARCOR coefficient mean values and the output mean-square error (MSE) are approximated and a simple model is described which approximates these quantities as functions of time. Calculated curves using this model are compared with simulation results. Results obtained for a two-stage lattice are then compared with the two-stage least mean-square (LMS) transversal filter algorithm, demonstrating that it is possible but unlikely for the transversal filter to converge faster than the analogous lattice filter.

Overflow oscillation in digital lattice filters

The overflow oscillation problem in fixed-point arithmetic digital lattice filters is considered. Conditions for overflow stability are formulated in the filter K-parameter space for the 2-multiplier and the 1-multiplier lattice filters, using their state-space description. It is found that the 2-multiplier lattice model is overflow stable over a much wider range of K-parameter than the canonical 1-multiplier model, and that the optimal choice of the sign paramethers cm of the latter as proposed by Markel and Gray sometimes makes the filter overflow unstable. However, both lattices are more stable than the direct form realisation.

Passive cascaded lattice digital filters

Energy and power analogies are used for the analysis of cascaded (possibly time-varying) lattice digital filters. This approach leads to the requirements for passivity of the sections, and a procedure for the removal of zero-input parasitic oscillations, along with several other results.

A class of generalized lattice filters

It is shown that the digital lattice filter utilized as a predictor in speech processing is a special case of a broad class of filters with identical properties in which the delay element is replaced by an arbitrary analog or digital all-pass filter. The performance of three filters in this class, the delay element and single-pole analog and digital all-pass sections, are compared for the special estimation application.

On the design of wave digital lattice filters with short coefficient word lengths and optimal dynamic range

Wave digital lattice filters require, in general, fewer multipliers than other digital realizations and have excellent passband sensitivity properties. Because of the variety of solutions which are possible for the realization of the lattice reactances, these filters can be designed with simple multiplier coefficients in spite of the high sensitivity in the stopband. The filter structure which offers the optimal dynamic range is determined by means of the equivalences between parallel and series adaptors and by means of scaling with coefficients equal to powers of two. This is illustrated by some specific examples.

A class of all-zero lattice digital filters: Properties and applications

A class of minimum- or maximum-phase all-zero lattice digital filters, based on the two-multiplier lattice of Itakura and Saito, is developed. Different lattice forms with different numbers of multipliers are derived, including two one-multiplier forms. Many of the properties of these lattice filters are given, including the important orthogonalization and decoupling properties of successive stages in optimal inverse filtering of signals. These properties lead to important applications in the areas of adaptive linear prediction and adaptive Wiener filtering. As a specific example, the design of a new fast start-up equalizer is presented.

Digital lattice and ladder filter synthesis

There is evidence that in addition to standard digital filter forms such as the direct, parallel, and cascade forms, digital lattice and ladder filters may play an important role in finite word length implementation problems. In this paper, techniques are developed in detail for efficiently synthesizing digital lattice and ladder filters from any stable direct form. In one form, a lattice filter canonic in terms of multiplies and delays is obtained. An internal scaling procedure is also introduced that will be of importance for optimizing one of the lattice forms for finite word length implementation.