Ronald E. Crochiere

Interpolation and decimation of digital signals—A tutorial review

The concepts of digital signal processing are playing an increasingly important role in the area of multirate signal processing, i.e. signal processing algorithms that involve more than one sampling rate. In this paper we present a tutorial overview of multirate digital signal processing as applied to systems for decimation and interpolation. We first discuss a theoretical model for such systems (based on the sampling theorem) and then show how various structures can be derived to provide efficient implementations of these systems. Design techniques for the linear-time-invariant components of these systems (the digital filter) are discussed, and finally the ideas behind multistage implementations for increased efficiency are presented.

Optimum FIR digital filter implementations for decimation, interpolation, and narrow-band filtering

In this paper a general theory of multistage decimators and interpolators for sampling rate reduction and sampling rate increase is presented. A set of curves and the necessary relations for optimally designing multistage decimators is also given. It is shown that the processes of decimation and interpolation are duals and therefore the same set of design curves applies to both problems. Further, it is shown that highly efficient implementations of narrow-band finite impulse response (FIR) filters can be obtained by cascading the processes of decimation and interpolation. Examples show that the efficiencies obtained are comparable to those of recursive elliptic filter designs.

A weighted overlap-add method of short-time Fourier analysis/Synthesis

In this correspondence we present a new structure and a simplified interpretation of short-time Fourier synthesis using synthesis windows. We show that this approach can be interpreted as a modification of the overlap-add method where we inverse the Fourier transform and window by the synthesis window prior to overlap-adding. This simplified interpretation results in a more efficient structure for short-time synthesis when a synthesis window is desired. In addition, we show how this structure can be used for analysis/synthesis applications which require different analysis and synthesis rates, such as time compression or expansion.

Analysis of linear digital networks

A framework is presented for the analysis, representation, and evaluation of digital filter structures. Based on the notation of linear signal-flow graphs and their equivalent matrix representation, a set of general linear digital network properties are reviewed, including precedence relations computability, Tellegens theorem, interreciprocity, and network transposition. These properties are then utilized in developing time and frequency domain analysis techniques and sensitivity analysis techniques. These techniques, in turn, are applied to the comparison of several basic digital filter structures.

Quadrature mirror filter design in the time domain

A new technique for designing quadrature mirror filters is described. The formulation, carried out in the time domain, is shown to result in an optimization problem requiring minimization of a quartic multinomial. An iterative solution is suggested which involves (computation of) the eigenvector of a matrix with a dimensionality equal to one half the number of filter taps. Our experiments show that convergence to the optimum tap weights is stable, and the accuracy of the final solution is limited only by the accuracy of the eigenvalue-eigenvector routine. As in an earlier technique, the user can specify the stop: band frequency the relative weights of the passband ripple energy and the stopband residual energy, and, of course, the number of filter taps.

A study of complexity and quality of speech waveform coders

This paper presents the results of a pilot study comparing four different speech waveform coding techniques of varying complexity. Coder transmission rates of 24, 16, and 9.6 Kb/s were used in the experiment. Subjective ratings and objective measurements of quality are obtained and compared. A number of conclusions are drawn concerning the quality and complexity, of different coding techniques. By comparing the objective measurements to the subjective ratings a number of conclusions are also drawn concerning the strengths and weaknesses of various (objective) quality measures of speech waveform coders.

Real-Time Speech Coding

This paper reviews our recent efforts in the design and implementation of real-time speech coders. We discuss our approach and methodology for real-time hardware for coder techniques ranging from low to high complexity. Examples of realizations are given for each approach. They include adaptive differential PCM coding, subband coding, harmonic scaling with subband coding, and adaptive transform coding. Low to medium complexity techniques are based on the use of the Bell Laboratories digital signal processing (DSP) integrated circuit. High complexity block processing techniques are based on the use of an array processing computer. We conclude with an assessment of the performance versus complexity tradeoffs involved in these coding methods.

FIR system modeling and identification in the presence of noise and with band-limited inputs

System identification, that is, the modeling and identification of a system from knowledge of its input and output signals, is a subject that is of considerable importance in many areas of signal and data processing. Because of the diversity of applications, a number of different methods for system identification with different advantages and disadvantages have been described and used in the literature. In this paper we investigate the performance of three well-known system identification methods based on an FIR (finite impulse response) model of the system. The methods will be referred to in this paper as the least squares analysis (LSA) method, the least mean squares adaptation algorithm (LMS), and the short-time spectral analysis (SSA) procedure. Our particular interest in this paper concerns the performance of these algorithms in the presence of high noise levels and in situations where the input signal may be band-limited. Both white and nonwhite random noise signals as well as speech signals are used as test signals to measure the performance of each of the system identification techniques as a function of the signal-to-noise ratio of the systems output. Quantitative results in terms of an accuracy measure of system identification are presented and a simple analytical model is used to explain the measured results.

A novel approach to the design of analysis/Synthesis filter banks

A novel technique for the design of analysis/synthesis filter banks, such as quadrature-mirror filter (QMF) banks, is presented. The technique is iterative, but each iteration step is mathematically simple. It is based upon a sectional approximation of the filter bank wherein the synthesis section is taken to be known from the previous iteration, and the analysis section is optimized according to the performance criterion. The strategy is then reversed, and the synthesis section optimized. At each iteration, each of these two steps results in an eigenvalue-eigenvector problem of a matrix with dimensionality equal to the number of taps. The technique is exemplified in detail for the QMF bank design problem.

An interpretation of the log likelihood ratio as a measure of waveform coder performance

The log likelihood measure has been widely used in speech research for comparing speech signals. Recently, it has been proposed as a measure for assessing the quality of coded speech. In this paper we present an interpretation of the log likelihood ratio measure within the theoretical framework of a waveform coder distortion model. We then discuss the implications of this interpretation and show how it can be applied to the formulation of better objective measures of waveform coder performance.