Lawrence R. Rabiner

An introduction to hidden Markov models

The basic theory of Markov chains has been known to mathematicians and engineers for close to 80 years, but it is only in the past decade that it has been applied explicitly to problems in speech processing. One of the major reasons why speech models, based on Markov chains, have not been developed until recently was the lack of a method for optimizing the parameters of the Markov model to match observed signal patterns. Such a method was proposed in the late 1960s and was immediately applied to speech processing in several research institutions. Continued refinements in the theory and implementation of Markov modelling techniques have greatly enhanced the method, leading to a wide range of applications of these models. It is the purpose of this tutorial paper to give an introduction to the theory of Markov models, and to illustrate how they have been applied to problems in speech recognition.

Hidden Markov models for speech recognition

The use of hidden Markov models for speech recognition has become predominant in the last several years, as evidenced by the number of published papers and talks at major speech conferences. The reasons this method has become so popular are the inherent statistical (mathematically precise) framework; the ease and availability of training algorithms for cstimating the parameters of the models from finite training sets of speech data; the flexibility of the resulting recognition system in which one can easily change the size, type, or architecture of the models to suit particular words, sounds, and so forth; and the ease of implementation of the overall recognition system. In this expository article, we address the role of statistical methods in this powerful technology as applied to speech recognition and discuss a range of theoretical and practical issues that are as yet unsolved in terms of their importance and their effect on performance for different system implementations.

A computer program for designing optimum FIR linear phase digital filters

This paper presents a general-purpose computer program which is capable of designing a large Class of optimum (in the minimax sense) FIR linear phase digital filters. The program has options for designing such standard filters as low-pass, high-pass, bandpass, and bandstop filters, as well as multipassband-stopband filters, differentiators, and Hilbert transformers. The program can also be used to design filters which approximate arbitrary frequency specifications which are provided by the user. The program is written in Fortran, and is carefully documented both by comments and by detailed flowcharts. The filter design algorithm is shown to be exceedingly efficient, e.g., it is capable of designing a filter with a 100-point impulse response in about 20 s.

A unified approach to short-time Fourier analysis and synthesis

Two distinct methods for synthesizing a signal from its short-time Fourier transform have previously been proposed. We call these methods the filter-bank summation (FBS) method and the overlap add (OLA) method. Each of these synthesis techniques has unique advantages and disadvantages in various applications due to the way in which the signal is reconstructed. In this paper we unify the ideas behind the two synthesis techniques and discuss the similarities and differences between these methods. In particular, we explicitly show the effects of modifications made to the short-time transform (both fixed and time-varying modifications are considered) on the resulting signal and discuss applications where each of the techniques would be most useful The interesting case of nonlinear modifications (possibly signal dependent) to the short-time Fourier transform is also discussed. Finally it is shown that a formal duality exists between the two synthesis methods based on the properties of the window used for obtaining the short-time Fourier transform.

A digital signal processing approach to interpolation

In many digital signal precessing systems, e.g., vacoders, modulation systems, and digital waveform coding systems, it is necessary to alter the sampling rate of a digital signal Thus it is of considerable interest to examine the problem of interpolation of bandlimited signals from the viewpoint of digital signal processing. A frequency dmnain interpretation of the interpolation process, through which it is clear that interpolation is fundamentally a linear filtering process, is presented, An examination of the relative merits of finite duration impulse response (FIR) and infinite duration impulse response (IIR) digital filters as interpolation filters indicates that FIR filters are generally to be preferred for interpolation. It is shown that linear interpolation and classical polynomial interpolation correspond to the use of the FIR interpolation filter. The use of classical interpolation methods in signal processing applications is illustrated by a discussion of FIR interpolation filters derived from the Lagrange interpolation formula. The limitations of these filters lead us to a consideration of optimum FIR filters for interpolation that can be designed using linear programming techniques. Examples are presented to illustrate the significant improvements that are obtained using the optimum filters.

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.

On the use of autocorrelation analysis for pitch detection

One of the most time honored methods of detecting pitch is to use some type of autocorrelation analysis on speech which has been appropriately preprocessed. The goal of the speech preprocessing in most systems is to whiten, or spectrally flatten, the signal so as to eliminate the effects of the vocal tract spectrum on the detailed shape of the resulting autocorrelation function. The purpose of this paper is to present some results on several types of (nonlinear) preprocessing which can be used to effectively spectrally flatten the speech signal The types of nonlinearities which are considered are classified by a non-linear input-output quantizer characteristic. By appropriate adjustment of the quantizer threshold levels, both the ordinary (linear) autocorrelation analysis, and the center clipping-peak clipping autocorrelation of Dubnowski et al. [1] can be obtained. Results are presented to demonstrate the degree of spectrum flattening obtained using these methods. Each of the proposed methods was tested on several of the utterances used in a recent pitch detector comparison study by Rabiner et al. [2] Results of this comparison are included in this paper. One final topic which is discussed in this paper is an algorithm for adaptively choosing a frame size for an autocorrelation pitch analysis.

Performance tradeoffs in dynamic time warping algorithms for isolated word recognition

The technique of dynamic programming for the time registration of a reference and a test pattern has found widespread use in the area of isolated word recognition. Recently, a number of variations on the basic time warping algorithm have been proposed by Sakoe and Chiba, and Rabiner, Rosenberg, and Levinson. These algorithms all assume that the test input is the time pattern of a feature vector from an isolated word whose endpoints are known (at least approximately). The major differences in the methods are the global path constraints (i.e., the region of possible warping paths), the local continuity constraints on the path, and the distance weighting and normalization used to give the overall minimum distance. The purpose of this investigation is to study the effects of such variations on the performance of different dynamic time warping algorithms for a realistic speech database. The performance measures that were used include: speed of operation, memory requirements, and recognition accuracy. The results show that both axis orientation and relative length of the reference and the test patterns are important factors in recognition accuracy. Our results suggest a new approach to dynamic time warping for isolated words in which both the reference and test patterns are linearly warped to a fixed length, and then a simplified dynamic time warping algorithm is used to handle the nonlinear component of the time alignment. Results with this new algorithm show performance comparable to or better than that of all other dynamic time warping algorithms that were studied.

A vector quantization approach to speaker recognition

In this study a vector quantization (VQ) codebook was used as an efficient means of characterizing the short-time spectral features of a speaker. A set of such codebooks were then used to recognize the identity of an unknown speaker from his/her unlabelled spoken utterances based on a minimum distance (distortion) classification rule. A series of speaker recognition experiments was performed using a 100-talker (50 male and 50 female) telephone recording database consisting of isolated digit utterances. For ten random but different isolated digits, over 98% speaker identification accuracy was achieved. The effects, on performance, of different system parameters such as codebook sizes, the number of test digits, phonetic richness of the text, and difference in recording sessions were also studied in detail.

The chirp z-transform algorithm

A computational algorithm for numerically evaluating the z -transform of a sequence of N samples is discussed. This algorithm has been named the chirp z -transform (CZT) algorithm. Using the CZT algorithm one can efficiently evaluate the z -transform at M points in the z -plane which lie on circular or spiral contours beginning at any arbitrary point in the z -plane. The angular spacing of the points is an arbitrary constant, and M and N are arbitrary integers. The algorithm is based on the fact that the values of the z -transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N+M) \log_{2}(N+M) as opposed to being proportional to N . M for direct evaluation of the z -transform at M points.