DOCSLIB.ORG

Weighted Automata in Text and Speech Processing

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Weighted Automata in Text and Speech Processing Weighted Automata in Text and Speech Processing Mehryar Mohri, Fernando Pereira, Michael Riley AT&T Research 600 Mountain Avenue Murray Hill, 07974 NJ {mohri,pereira,riley}@research.att.com Abstract. Finite-state automata are a very effective tool level. In particular, we use transducer composition to repre- in natural language processing. However, in a variety of ap- sent the combination of the various levels of acoustic, phonetic plications and especially in speech precessing, it is necessary and linguistic information used in a recognizer [11]. For exam- to consider more general machines in which arcs are assigned ple, we may decompose a recognition task into a weighted ac- weights or costs. We briefly describe some of the main theoret- ceptor O describing the acoustic observation sequence for the ical and algorithmic aspects of these machines. In particular, utterance to be recognized, a transducer A mapping acoustic we describe an efficient composition algorithm for weighted observation sequences to context-dependent phone sequences, transducers, and give examples illustrating the value of de- a transducer C that converts between sequences of context- terminization and minimization algorithms for weighted au- dependent and context-independent phonetic units, a trans- tomata. ducer D from context-independent unit sequences to word sequences and a weighted acceptor M that specifies the lan- guage model 1 Introduction , that is, the likelihoods of different lexical tran- scriptions (Figure 2). Finite-state acceptors and transducers have been successfully used in many natural language-processing applications, for o1 o2 on (a) t t t ... t instance the compilation of morphological and phonological 0 1 2 n rules [5, 10] and the compact representation of very large dic- tionaries [8, 12]. An important reason for those successes is ε ε oi: /p01(i) oi: /p12(i) ε:π/p2f that complex acceptors and transducers can be conveniently (b) s s s 0 . 1 . 2 built from simpler ones by using a standard set of algebraic . operations — the standard rational operations together with . transducer composition — that can be efficiently implemented o :ε/p (i) o :ε/p (i) o :ε/p (i) [4, 2]. However, applications such as speech processing re- i 00 i 11 i 22 quire the use of more general devices: weighted acceptors and ε ε weighted transducers, that is, automata in which transitions d:ε/1 ey: /.4 dx: /.8 ax:"data"/1 (c) are assigned a weight in addition to the usual transition la- ae:ε/.6 t:ε/.2 bels. We briefly sketch here the main theoretical and algo- rithmic aspects of weighted acceptors and transducers and α:π their application to speech processing. Our novel contribu- .c γ π . : r . (d) . qlc qcr . tions include a general way of representing recognition tasks ω:π . c . with weighted transducers, the use of transducers to repre- . β:πs . sent context-dependencies in recognition, efficient algorithms qcs . for on-the-fly composition of weighted transducers, and effi- cient algorithms for determinizing and minimizing weighted automata, including an on-the-fly determinization algorithm Figure 1. Models as Weighted Transducers. to remove redundancies in the interface between a recognizer and subsequent language processing. The trivial acoustic observation acceptor O for the vector- 2 Speech processing quantized representation of a given utterance is depicted in Figure 1a. Each state represents a point in time ti, and the In our work we use weighted automata as a simple and ef- transition from ti−1 to ti is labeled with the name oi of the ficient representation for all the inputs, outputs and domain quantization cell that contains the acoustic parameter vector information in speech recognition above the signal processing for the sample at time ti−1. For continuous-density acoustic c 1996 AT&T Corp. ECAI 96. 12th European Conference on Artificial Intelligence Edited by W. Wahlster Published in 1996 by John Wiley & Sons, Ltd. O A C D M Context− Observations dependent phones words sentences phones Figure 2. Recognition Cascade representations, there would be a transition from ti−1 to ti la- Finite-state models have been used widely in speech recog- beled with a distribution name and the likelihood1of that dis- nition for quite a while, in the form of hidden-Markov models tribution generating the acoustic-parameter vector, for each and related probabilistic automata for acoustic modeling [1] acoustic-parameter distribution in the acoustic model. and of various probabilistic language models. However, our The acoustic-observation sequence to phone sequence trans- approach of expressing the recognition task with transducer ducer A is built from context-dependent (CD) phone models. composition and of representing context dependencies with A CD-phone model is given as a transducer from a sequence transducers allows a new flexibility and greater uniformity of acoustic observation labels to a specific context-dependent and modularity in building and optimizing recognizers. unit, and assigns to each acoustic sequence the likelihood that the specified unit produced it. Thus, different paths through a CD-phone model correspond to different acoustic realizations 3 Theoretical definitions of a CD-phone. Figure 1b depicts a common topology for such a CD-phone model. The full acoustic-to-phone transducer A is In a recognition cascade such as the one we just discussed then defined by an appropriate algebraic combination (Kleene (Figure 2), each step implements a mapping from input-output closure of sum) of CD-phone models. pairs (r, s) to probabilities P (s|r). More formally, each trans- The form of C for triphonic CD-models is depicted in Fig- ducer in the cascade implements a weighted transduction. A ure 1d. For each context-dependent phone model γ, which weighted transduction T is a mapping T :Σ∗ ×Γ∗ → K where ∗ ∗ corresponds to the (context-independent) phone πc in the con- Σ and Γ are the sets of strings over the alphabets Σ and text of πl and πr, there is a state qlc in C for the biphone πlπc, Γ, and K is an appropriate weight structure, for instance the 2 a state qcr for πcπr and a transition from qlc to qcr with in- real numbers between 0 and 1 in the case of probabilities. put label γ and output label πr. We have used transducers of The right-most step of (Figure 2), the language model ac- that and related forms to map context-independent phonetic ceptor M, represents not a transduction but a weighted lan- representations to context-dependent representations for a va- guage. However, we can identify any weighted language L with riety of medium to large vocabulary speech recognition tasks. the restriction of the identity transduction that assigns to We are thus able to provide full-context dependency, with its (w,w) the same weight as L assigns to w, and in the rest of well-known accuracy advantages [7], without having to build the paper we will use this to identify languages with trans- special-purpose context-dependency machinery in the recog- ductions and acceptors with transducers as appropriate. nizer. Given two transductions S : Σ∗ × Γ∗ → K and T : Γ∗ × The transducer D from phone sequences to word sequences ∆∗ → K, we can define their composition S ◦ T by is defined similarly to A. We first build word models as trans- ducers from sequences of phone labels to a specific word, (S ◦ T )(r, t) = X S(r, s)T (s, t) (1) which assign to each phone sequence a likelihood that the s∈Γ∗ specified word produced it. Thus, different paths through a word model correspond to different phonetic realizations of For example, if S represents P (sl|si) and T P (sj |sl) in (2), the word. Figure 1c shows a typical word model. D is then S ◦ T represents P (sj |si). defined as an appropriate algebraic combination of word mod- It is easy to see that composition ◦ is associative, that is, in els. any transduction cascade R1 ◦· · ·◦Rm, the order of association Finally, the language model M, which may be for example of the ◦ operators does not matter. an n-gram model of word sequence statistics, is easily repre- Rational weighted transductions and languages are those sented as a weighted acceptor. that can be defined by application of appropriate generaliza- The overall recognition task can be then expressed as the tions of the standard Kleene operations (union-sum, concate- search for the highest-likelihood string in the composition nation and closure) and are also exactly those implemented O ◦ A ◦ C ◦ D ◦ M of the various transducers just described, by weighted finite-state automata (transducers and acceptors) which is an acceptor assigning each word sequence the likeli- [4, 3, 6]. We are thus justified in our abuse of language in us- hood that it could have generated the given acoustic observa- ing the same terms and symbols for rational transduction and tions. For efficiency, we use the standard Viterbi approxima- finite-state transducer operations in what follows. tion and search for the highest-probability path rather than the highest-probability string. 1 For computational reasons, sums and products of probabilities are often replaced by minimizations and sums of negative log probabilities. Formally, this corresponds to changing the semir- 2 Composition can be defined for any semiring (K, +, ·), and the ing of the weights. The algorithms we present here work for any transductions we are considering here can be defined in terms of semiring. formal power series [3, 6]. 2 M. Mohri, F. Pereira and M. Riley 4 Efficient Composition of Weighted Finite-State Transducers (a) a:a b:ε c:ε d:d A 0 1 2 3 4 Composition is the key operation on weighted transducers.
Load more

Recommended publications
  • Speech Signal Basics
    Speech Signal Basics Nimrod Peleg Updated: Feb. 2010 Course Objectives • To get familiar with: – Speech coding in general – Speech coding for communication (military, cellular) • Means: – Introduction the basics of speech processing – Presenting an overview of speech production and hearing systems – Focusing on speech coding: LPC codecs: • Basic principles • Discussing of related standards • Listening and reviewing different codecs. הנחיות לשימוש נכון בטלפון, פלשתינה-א"י, 1925 What is Speech ??? • Meaning: Text, Identity, Punctuation, Emotion –prosody: rhythm, pitch, intensity • Statistics: sampled speech is a string of numbers – Distribution (Gamma, Laplace) Quantization • Information Theory: statistical redundancy – ZIP, ARJ, compress, Shorten, Entropy coding… ...1001100010100110010... • Perceptual redundancy – Temporal masking , frequency masking (mp3, Dolby) • Speech production Model – Physical system: Linear Prediction The Speech Signal • Created at the Vocal cords, Travels through the Vocal tract, and Produced at speakers mouth • Gets to the listeners ear as a pressure wave • Non-Stationary, but can be divided to sound segments which have some common acoustic properties for a short time interval • Two Major classes: Vowels and Consonants Speech Production • A sound source excites a (vocal tract) filter – Voiced: Periodic source, created by vocal cords – UnVoiced: Aperiodic and noisy source •The Pitch is the fundamental frequency of the vocal cords vibration (also called F0) followed by 4-5 Formants (F1 -F5) at higher frequencies.
    [Show full text]
  • Benchmarking Audio Signal Representation Techniques for Classification with Convolutional Neural Networks
    sensors Article Benchmarking Audio Signal Representation Techniques for Classification with Convolutional Neural Networks Roneel V. Sharan * , Hao Xiong and Shlomo Berkovsky Australian Institute of Health Innovation, Macquarie University, Sydney, NSW 2109, Australia; [email protected] (H.X.); [email protected] (S.B.) * Correspondence: [email protected] Abstract: Audio signal classification finds various applications in detecting and monitoring health conditions in healthcare. Convolutional neural networks (CNN) have produced state-of-the-art results in image classification and are being increasingly used in other tasks, including signal classification. However, audio signal classification using CNN presents various challenges. In image classification tasks, raw images of equal dimensions can be used as a direct input to CNN. Raw time- domain signals, on the other hand, can be of varying dimensions. In addition, the temporal signal often has to be transformed to frequency-domain to reveal unique spectral characteristics, therefore requiring signal transformation. In this work, we overview and benchmark various audio signal representation techniques for classification using CNN, including approaches that deal with signals of different lengths and combine multiple representations to improve the classification accuracy. Hence, this work surfaces important empirical evidence that may guide future works deploying CNN for audio signal classification purposes. Citation: Sharan, R.V.; Xiong, H.; Berkovsky, S. Benchmarking Audio Keywords: convolutional neural networks; fusion; interpolation; machine learning; spectrogram; Signal Representation Techniques for time-frequency image Classification with Convolutional Neural Networks. Sensors 2021, 21, 3434. https://doi.org/10.3390/ s21103434 1. Introduction Sensing technologies find applications in detecting and monitoring health conditions.
    [Show full text]
  • Designing Speech and Multimodal Interactions for Mobile, Wearable, and Pervasive Applications
    Designing Speech and Multimodal Interactions for Mobile, Wearable, and Pervasive Applications Cosmin Munteanu Nikhil Sharma Abstract University of Toronto Google, Inc. Traditional interfaces are continuously being replaced Mississauga [email protected] by mobile, wearable, or pervasive interfaces. Yet when [email protected] Frank Rudzicz it comes to the input and output modalities enabling Pourang Irani Toronto Rehabilitation Institute our interactions, we have yet to fully embrace some of University of Manitoba University of Toronto the most natural forms of communication and [email protected] [email protected] information processing that humans possess: speech, Sharon Oviatt Randy Gomez language, gestures, thoughts. Very little HCI attention Incaa Designs Honda Research Institute has been dedicated to designing and developing spoken [email protected] [email protected] language and multimodal interaction techniques, Matthew Aylett Keisuke Nakamura especially for mobile and wearable devices. In addition CereProc Honda Research Institute to the enormous, recent engineering progress in [email protected] [email protected] processing such modalities, there is now sufficient Gerald Penn Kazuhiro Nakadai evidence that many real-life applications do not require University of Toronto Honda Research Institute 100% accuracy of processing multimodal input to be [email protected] [email protected] useful, particularly if such modalities complement each Shimei Pan other. This multidisciplinary, two-day workshop
    [Show full text]
  • Introduction to Digital Speech Processing Schafer Rabiner and Ronald W
    SIGv1n1-2.qxd 11/20/2007 3:02 PM Page 1 FnT SIG 1:1-2 Foundations and Trends® in Signal Processing Introduction to Digital Speech Processing Processing to Digital Speech Introduction R. Lawrence W. Rabiner and Ronald Schafer 1:1-2 (2007) Lawrence R. Rabiner and Ronald W. Schafer Introduction to Digital Speech Processing highlights the central role of DSP techniques in modern speech communication research and applications. It presents a comprehensive overview of digital speech processing that ranges from the basic nature of the speech signal, through a variety of methods of representing speech in digital form, to applications in voice communication and automatic synthesis and recognition of speech. Introduction to Digital Introduction to Digital Speech Processing provides the reader with a practical introduction to Speech Processing the wide range of important concepts that comprise the field of digital speech processing. It serves as an invaluable reference for students embarking on speech research as well as the experienced researcher already working in the field, who can utilize the book as a Lawrence R. Rabiner and Ronald W. Schafer reference guide. This book is originally published as Foundations and Trends® in Signal Processing Volume 1 Issue 1-2 (2007), ISSN: 1932-8346. now now the essence of knowledge Introduction to Digital Speech Processing Introduction to Digital Speech Processing Lawrence R. Rabiner Rutgers University and University of California Santa Barbara USA [email protected] Ronald W. Schafer Hewlett-Packard Laboratories Palo Alto, CA USA Boston – Delft Foundations and Trends R in Signal Processing Published, sold and distributed by: now Publishers Inc.
    [Show full text]
  • Models of Speech Synthesis ROLF CARLSON Department of Speech Communication and Music Acoustics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
    Proc. Natl. Acad. Sci. USA Vol. 92, pp. 9932-9937, October 1995 Colloquium Paper This paper was presented at a colloquium entitled "Human-Machine Communication by Voice," organized by Lawrence R. Rabiner, held by the National Academy of Sciences at The Arnold and Mabel Beckman Center in Irvine, CA, February 8-9,1993. Models of speech synthesis ROLF CARLSON Department of Speech Communication and Music Acoustics, Royal Institute of Technology, S-100 44 Stockholm, Sweden ABSTRACT The term "speech synthesis" has been used need large amounts of speech data. Models working close to for diverse technical approaches. In this paper, some of the the waveform are now typically making use of increased unit approaches used to generate synthetic speech in a text-to- sizes while still modeling prosody by rule. In the middle of the speech system are reviewed, and some of the basic motivations scale, "formant synthesis" is moving toward the articulatory for choosing one method over another are discussed. It is models by looking for "higher-level parameters" or to larger important to keep in mind, however, that speech synthesis prestored units. Articulatory synthesis, hampered by lack of models are needed not just for speech generation but to help data, still has some way to go but is yielding improved quality, us understand how speech is created, or even how articulation due mostly to advanced analysis-synthesis techniques. can explain language structure. General issues such as the synthesis of different voices, accents, and multiple languages Flexibility and Technical Dimensions are discussed as special challenges facing the speech synthesis community.
    [Show full text]
  • Audio Processing Laboratory
    AC 2010-1594: A GRADUATE LEVEL COURSE: AUDIO PROCESSING LABORATORY Buket Barkana, University of Bridgeport Page 15.35.1 Page © American Society for Engineering Education, 2010 A Graduate Level Course: Audio Processing Laboratory Abstract Audio signal processing is a part of the digital signal processing (DSP) field in science and engineering that has developed rapidly over the past years. Expertise in audio signal processing - including speech signal processing- is becoming increasingly important for working engineers from diverse disciplines. Audio signals are stored, processed, and transmitted using digital techniques. Creating these technologies requires engineers that understand real-time application issues in the related areas. With this motivation, we designed a graduate level laboratory course which is Audio Processing Laboratory in the electrical engineering department in our school two years ago. This paper presents the status of the audio processing laboratory course in our school. We report the challenges that we have faced during the development of this course in our school and discuss the instructor’s and students’ assessments and recommendations in this real-time signal-processing laboratory course. 1. Introduction Many DSP laboratory courses are developed for undergraduate and graduate level engineering education. These courses mostly focus on the general signal processing techniques such as quantization, filter design, Fast Fourier Transformation (FFT), and spectral analysis [1-3]. Because of the increasing popularity of Web-based education and the advancements in streaming media applications, several web-based DSP Laboratory courses have been designed for distance education [4-8]. An internet-based signal processing laboratory that provides hands-on learning experiences in distributed learning environments has been developed by Spanias et.al[6] .
    [Show full text]
  • ECE438 - Digital Signal Processing with Applications 1
    Purdue University: ECE438 - Digital Signal Processing with Applications 1 ECE438 - Laboratory 9: Speech Processing (Week 1) October 6, 2010 1 Introduction Speech is an acoustic waveform that conveys information from a speaker to a listener. Given the importance of this form of communication, it is no surprise that many applications of signal processing have been developed to manipulate speech signals. Almost all speech processing applications currently fall into three broad categories: speech recognition, speech synthesis, and speech coding. Speech recognition may be concerned with the identification of certain words, or with the identification of the speaker. Isolated word recognition algorithms attempt to identify individual words, such as in automated telephone services. Automatic speech recognition systems attempt to recognize continuous spoken language, possibly to convert into text within a word processor. These systems often incorporate grammatical cues to increase their accuracy. Speaker identification is mostly used in security applications, as a person’s voice is much like a “fingerprint”. The objective in speech synthesis is to convert a string of text, or a sequence of words, into natural-sounding speech. One example is the Speech Plus synthesizer used by Stephen Hawking (although it unfortunately gives him an American accent). There are also similar systems which read text for the blind. Speech synthesis has also been used to aid scientists in learning about the mechanisms of human speech production, and thereby in the treatment of speech-related disorders. Speech coding is mainly concerned with exploiting certain redundancies of the speech signal, allowing it to be represented in a compressed form. Much of the research in speech compression has been motivated by the need to conserve bandwidth in communication sys- tems.
    [Show full text]
  • Speech Processing Based on a Sinusoidal Model
    R.J. McAulay andT.F. Quatieri Speech Processing Based on a Sinusoidal Model Using a sinusoidal model of speech, an analysis/synthesis technique has been devel­ oped that characterizes speech in terms of the amplitudes, frequencies, and phases of the component sine waves. These parameters can be estimated by applying a simple peak-picking algorithm to a short-time Fourier transform (STFf) of the input speech. Rapid changes in the highly resolved spectral components are tracked by using a frequency-matching algorithm and the concept of"birth" and "death" ofthe underlying sinewaves. Fora givenfrequency track, a cubic phasefunction is applied to a sine-wave generator. whose outputis amplitude-modulated andadded to the sine waves generated for the other frequency tracks. and this sum is the synthetic speech output. The resulting waveform preserves the general waveform shape and is essentially indistin­ gUishable from the original speech. Furthermore. inthe presence ofnoise the perceptual characteristics ofthe speech and the noise are maintained. Itwas also found that high­ quality reproduction was obtained for a large class of inputs: two overlapping. super­ posed speech waveforms; music waveforms; speech in musical backgrounds; and certain marine biologic sounds. The analysis/synthesis system has become the basis for new approaches to such diverse applications as multirate coding for secure communications, time-scale and pitch-scale algorithms for speech transformations, and phase dispersion for the enhancement ofAM radio broadcasts. Moreover, the technology behind the applications has been successfully transferred to private industry for commercial development. Speech signals can be represented with a Other approaches to analysis/synthesis that· speech production model that views speech as are based on sine-wave models have been the result of passing a glottal excitation wave­ discussed.
    [Show full text]
  • Edinburgh Research Explorer
    Edinburgh Research Explorer Designing Speech and Multimodal Interactions for Mobile, Wearable, and Pervasive Applications Citation for published version: Munteanu, C, Irani, P, Oviatt, S, Aylett, M, Penn, G, Pan, S, Sharma, N, Rudzicz, F, Gomez, R, Nakamura, K & Nakadai, K 2016, Designing Speech and Multimodal Interactions for Mobile, Wearable, and Pervasive Applications. in Proceedings of the 2016 CHI Conference Extended Abstracts on Human Factors in Computing Systems. CHI EA '16, ACM, New York, NY, USA, pp. 3612-3619, 2016 CHI Conference Extended Abstracts on Human Factors in Computing Systems, San Jose, United States, 7/05/16. https://doi.org/10.1145/2851581.2856506 Digital Object Identifier (DOI): 10.1145/2851581.2856506 Link: Link to publication record in Edinburgh Research Explorer Document Version: Peer reviewed version Published In: Proceedings of the 2016 CHI Conference Extended Abstracts on Human Factors in Computing Systems General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 28. Sep. 2021 Designing Speech and Multimodal Interactions for Mobile, Wearable, and Pervasive Applications Cosmin Munteanu Nikhil Sharma University of Toronto Google, Inc.
    [Show full text]
  • Speech Processing and Prosody Denis Jouvet
    Speech Processing and Prosody Denis Jouvet To cite this version: Denis Jouvet. Speech Processing and Prosody. TSD 2019 - 22nd International Conference of Text, Speech and Dialogue, Sep 2019, Ljubljana, Slovenia. hal-02177210 HAL Id: hal-02177210 https://hal.inria.fr/hal-02177210 Submitted on 8 Jul 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Speech Processing and Prosody Denis Jouvet Universite´ de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France {denis.jouvet}@loria.fr Abstract. The prosody of the speech signal conveys information over the lin- guistic content of the message: prosody structures the utterance, and also brings information on speaker’s attitude and speaker’s emotion. Duration of sounds, en- ergy and fundamental frequency are the prosodic features. However their auto- matic computation and usage are not obvious. Sound duration features are usu- ally extracted from speech recognition results or from a force speech-text align- ment. Although the resulting segmentation is usually acceptable on clean native speech data, performance degrades on noisy or not non-native speech. Many algo- rithms have been developed for computing the fundamental frequency, they lead to rather good performance on clean speech, but again, performance degrades in noisy conditions.
    [Show full text]
  • Linear Prediction Analysis of Speech
    Appendix A Linear Prediction Analysis of Speech Linear prediction (LP) is one of the most important tools in speech analysis. The philosophy behind linear prediction is that a speech sample can be approximated as a linear combination of past samples. Then, by minimizing the sum of the squared differences between the actual speech samples and the linearly predicted ones over a finite interval, a unique set of predictor coefficients can be determined [15]. LP analysis decomposes the speech into two highly independent components, the vocal tract parameters (LP coefficients) and the glottal excitation (LP residual). It is assumed that speech is produced by exciting a linear time-varying filter (the vocal tract) by random noise for unvoiced speech segments, or a train of pulses for voiced speech. Figure A.1 shows a model of speech production for LP analysis [163]. It consists of a time varying filter H(z) which is excited by either a quasi periodic or a random noise source. The most general predictor form in linear prediction is the autoregressive moving average (ARMA) model where the speech sample s(n) is modelled as a linear combination of the past outputs and the present and past inputs [164–166]. It can be written mathematically as follows p q s(n)=− ∑ aks(n − k)+G ∑ blu(n − l), b0 = 1(A.1) k=1 l=0 where ak,1 ≤ k ≤ p,bl,1 ≤ l ≤ q and gain G are the parameters of the filter. Equivalently, in frequency domain, the transfer function of the linear prediction speech model is [164] q −l 1 + ∑ blz ( )= l=1 .
    [Show full text]
  • Speech Recognition Using Neural Networks
    SPEECH RECOGNITION USING NEURAL NETWORKS by Pablo Zegers _____________________________ Copyright © Pablo Zegers 1998 A Thesis Submitted to the Faculty of the DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING In Partial Fulfillment of the Requirements For the degree of MASTER OF SCIENCE WITH A MAJOR IN ELECTRICAL ENGINEERING In the Graduate College THE UNIVERSITY OF ARIZONA 1 9 9 8 2 STATEMENT BY AUTHOR This Thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the copyright holder. SIGNED: _________________________________ APPROVAL BY THESIS DIRECTOR This Thesis has been approved on the date shown below: ________________________________ ________________________________ Malur K. Sundareshan Date Professor of Electrical and Computer Engineering DEDICATION To God, “for thou hast made us for thyself and restless is our heart until it comes to rest in thee.” Saint Augustine, Confessions 4 TABLE OF CONTENTS 1. INTRODUCTION .................................................................................................................................. 11 1.1 LANGUAGES.......................................................................................................................................
    [Show full text]