ࡱ>  yVRoot Entryt+51N]^  F8xData/0(xX P`Z WordDocument 0qHC2pObjectPooloJ!yepffwpcpD$P  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !$%&'()*+,-./12efghijklmnopqrstuvwxyz{|}~VisioInformation"aSummaryInformation(b1TablezuSummaryInformation'((e#0DocumentSummaryInformation8FlCompObjNativetX0Table405FdtPICT v [(@(Normal$mH <@< Heading 1$$xx5CJ:@: Heading 2 $xx5CJ:: Heading 3 $<5CJ<< Heading 4 $< 56CJ>> Heading 5 <CJOJQJkHBB Heading 6 <6CJOJQJkH:: Heading 7 < OJQJkH>> niques have just been implemented and modified in order to be applicable to the Thai language as well. Recently, many research works on Thai speech processing have being conducted on the speaker-independent Thai isolated word recognition especially on the Thai numerals. And also some researches on the speaker-independent Thai connected word recognition have already been studied. The feature extraction and recognition techniques have been modified to accommodate the specific characteristics of Thai language especially the tonal characteristic as shown in Figure 1. This article is organized as follows. In Section 2, the Thai speech recognition model is proposed and described. In Section 3, the Thai speech analysis techniques are introduced. In Section 4, the Thai speech recognition techniques and result are compared and discussed. In Section 5, the future research directions are proposed. Finally, the conclusion of the speech recognition research in Thailand and the summary of all Thai speech recognition researches is shown in Table 2 and the 70 polysyllabic words vocabulary is shown in Table 3 at the end of this article.  EMBED Visio.Drawing.4  Figure 1. Five Thai Tonal Levels in Thai. (Luksaneeyanawin, 1993) EMBED MSGraph.Chart.5 \s  Figure 2. Energy Level Contour and Thresholds. (Ahkuputra, 1997) 2. Thai Speech Recognition Model The speech recognition model is based on the general statistical pattern recognition model. This particular model has been modified in order to be applicable to any speech recognition tasks and has been used extensively in almost every speech recognition system. For Thai language, the Thai speech recognition model as shown in Figure 8 and 9 have also been derived from that particular model. Various recognition techniques have been employed based on that model (Pensiri and Jitapunkul, 1995; Phatrapornnant and Jitapunkul, 1995; Areepongsa and Jitapunkul, 1995; Ahkuputra and Jitapunkul, 1997; Pornsukchandra and Jitapunkul, 1996) such as the Dynamic Time Warping (Pensiri and Jitapunkul, 1995; Phatrapornnant and Jitapunkul, 1995), the Hidden Markov Model (Areepongsa and Jitapunkul, 1995; Ahkuputra and Jitapunkul, 1997), and the Neural Network (Pornsukchandra and Jitapunkul, 1996; Wutiwiwatchai, 1997), for instance. In Figure 7, the model has been adapted to recognize the isolated Thai numerals using different recognition approaches. In Figure 8, the Hidden Markov Model technique has been employed in the recognition of 70 Thai polysyllabic words as shown in Table 2 and the model has been adapted to accommodate this specific technique. These two recognition models have been proved to be appropriate for Thai language as well. The details of each technique employs in the speech recognition model as shown in the two figures will be described in details in the next section. The speech recognition model consists of three major parts namelythe feature measurement, the pattern classification, and the decision rule. The additional signal preprocessing stage has been added to the model before the feature measurement stage. The purpose of the signal preprocessing is to prepare the input speech signal into a proper format for further processing. The processes of the signal preprocessing are signal preemphasis, frame blocking analysis, and smoothing window analysis. In the feature measurement stage, the speech features are extracted from the preprocessed speech samples using various feature extraction techniques such as the linear predictive coding (LPC), cepstral analysis, for instance. In the pattern classification and decision rule stages, various recognition approaches could be implemented as mentioned above. Details of each technique is given in the next section. 3. Thai Speech Analysis The speech analysis of Thai language plays a major role in Thai speech recognition. The speech features are extracted from the speech waveforms in order to represent the specific characteristics of Thai language. Various feature extraction techniques have been studied and applied to Thai language. Also, the endpoint detection techniques have been employed to find the speech boundaries over the waveform as follows. 3.1 Fast Fourier Transform Technique The Fast Fourier Fransform (FFT) and the Discrete Fourier Transform (DFT) have been used extensively in spectral analysis and also in the tonal analysis of Thai language for toneme recognition (Phatrapornnant and Jitapunkul, 1995). This will provide the distinctive tonal feature of Thai word as a linguistic information included in the recognition process. The autocorrelation function ((m) as shown in (1) is computed from the sampled time sequence x(n). The short-time spectrum S(() can be computed from the autocorrelation function as shown in (2) where ( is the normalized angle frequency. The short-time specture could be computed directly from the speech samples using the DFT facilitated by the FFT algorithm as shown in (3) as follows.  EMBED Equation.3  (1)  EMBED Equation.3  (2)  EMBED Equation.3  (3) 3.2 Discrete Hartley Transform Technique The Discrete Hartley Fransform (DHT) has also been studied and employed in the feature extraction of speech features from speech waveform (Pensiri and Jitapunkul, 1995). The computed DHT parameters are normalized and quantized into the discrete feature values. Then the speech waveform will be represented by the sequence of the feature values. The definition of the DHT has been defined as shown in (4) where  EMBED Equation.2  and N is the number of samples in a frame as follows.  EMBED Equation.2  (4) Table 1. The speech feature value of the normalized Discrete Hartley Transform value Feature ValueRange of  EMBED Equation.2  Value00.00 - 0.5010.50 - 1.0021.00 - 1.5031.50 - 2.0042.00 - 2.5052.50 - 3.0063.00 - 3.5073.50 - 4.0084.00 - 4.5094.50 - 5.00105.00 - 5.50115.50 - 6.00126.00 - 6.50136.50 - 7.00147.00 - 7.50157.50 and up The DHT values are computed from each frame with 50% frame overlaping. Then, the absolute DHT values are computed as shown in (5) where i is the order of frame and k is the DHT parameter order for 512-point DHT values. The absolute DHT values are then normalized with the average absolute DHT value as shown in (6). The speech feature value of each normalized DHT value is computed using the simple look-up table that assign the normalized DHT value within the range to a value as shown in Table 1. There are 15 speech feature values corresponding to 15 ranges of normalized DHT value. Then the speech feature sequence will be created accordingly.  EMBED Equation.2  (5)  EMBED Equation.2  (6) 3.3 Linear Prediction Analysis The linear prediction coefficient analysis has been widely employed in speech recognition systems (Areepongsa and Jitapunkul, 1995; Ahkuputra and Jitapunkul, 1997; Pornsukchandra and Jitapunkul, 1996; Prathumthan, 1986). This technique has been proved to be practical in speech feature extraction with precise vocal tract modelling. The commonly used analytical methods are the Levinson-Durbin and the PARCOR methods. The Levinson-Durbin recursive algorithm (OShaughnessy, 1988) is shown in (7) to (11) where am, 1 ( m ( p are the LPC coefficients, p is the number of LPC coefficients or the LPC orders, km is the reflection coefficient or the PARCOR coefficient, and gm is the log area ratio coefficient as follows.  EMBED Equation.2  (7)  EMBED Equation.2  (8)  EMBED Equation.2  (9)  EMBED Equation.2  (10)  EMBED Equation.2  (11) 3.4 Cepstral Analysis The Cepstral Analysis technique has also been applied in the current research on Thai speech recognition using the LPC-derived Cepstral Analysis. This approach makes use of the existing linear prediction coefficients to compute the ceptral coefficients (Furui, 1985; Rabiner and Juang, 1993; Rabiner and Schafer, 1978). The recursive algorithm is shown as follows (Furui, 1985).  EMBED Equation.2  (12)  EMBED Equation.2  (13)  EMBED Equation.2  (14) The cepstrum or cepstral coefficient c(() is defined as the inverse fourier transform of the short-time logarithmic amplitude spectrum (Ahkuputra and Jitapunkul, 1997). Let x(t) is the voiced speech which can be regarded as the response of the vocal tract articulation equivalent filter driven by a pseudoperiodic source g(t) and the vocal tract impulse response h(t) as shown in (12)-(15) where (-1 is the Inverse Fourier Transform. When the Discrete Fourier Transform (DFT) is used in stead of the Fourier Transform, the cepstram can be calculated as shown in (18).  EMBED Equation.2  (15)  EMBED Equation.2  (16)  EMBED Equation.2  (17)  EMBED Equation.2  (18) 3.5 Endpoint Detection Technique There are various techniques that have been implemented in the endpoint detection analysis such as fundamental frequency (F0), energy contour, zero crossing, formant tracking, speech duration, etc. These techniques are then combined in the endpoint detection analysis to find the speech boundaries of a word and segmentation of speech waveform into syllable units down to phoneme units (Areepongsa and Jitapunkul, 1995; Ahkuputra and Jitapunkul, 1997; Pornsukchandra and Jitapunkul, 1996; Prathumthan, 1986). The endpoint detection process is one of the most important procedure in isolated-word and connected-word recognition and also in the continuous speech recognition as well. The current implemented endpoint detection techniques applied to the Thai speech recognition are the Energy Level Contour and the Energy Level Threshold techniques. (Pensiri and Jitapunkul, 1995; Areepongsa and Jitapunkul, 1995; Ahkuputra and Jitapunkul, 1997; Pornsukchandra and Jitapunkul, 1996; Prathumthan, 1986; Wutiwiwatchai, 1987). In the energy level contour analysis, the energy value E(m) of the mth speech frame is computed as a sum of the absolute value of each speech sample s(n) within a frame as shown in (16). The energy level threshold is used as a guideline to keep track of the beginning point and ending point of each syllables in the word as shown in Figure 2.  EMBED Equation.2  (19) 3.6 Phonemic Distinctive Features This technique has been studied and applied to Thai speech analysis and recognition of Thai vowels, Thai consonants, and Thai tones (Thubthong, 1995) as shown in Table 1. The F0 direction and F0 height have been applied in tone phonemes recognition. On the vowel phoneme recognition, the F1, F2, and vowel duration have been employed as features. On the consonant recognition, there are many speech features have been utilized--the zero crossing, extremely high or low amplitude, acoustic energy, noise duration, burst duration, acoustic silence, and the F2 at transition zone between consonant and vowel. 4. Thai Speech Recognition The speech recognition approaches for Thai language have been implemented using various recognition techniques used extensively in English language, for instance, the Dynamic Time Warping (DTW), the Hidden Markov Model (HMM), the Neural Networks (NN), the Fuzzy Logic, etc. Excellent recognition results could be obtained on Thai speech recognition using these techniques. The details on these applied techniques are as follows. 4.1 Dynamic Time Warping The Dynamic Time Warping (DTW) technique has been studied and employed in many speaker independent Thai numerals recognition researches. (Pensiri and Jitapunkul, 1995; Phatrapornnant and Jitapunkul, 1995) The first research work utilizes this technique in conjunction with the Discrete Hartley Transform (DHT) for speech feature extraction to recognize ten Thai numerals from zero to nine. (Pensiri and Jitapunkul, 1995) The DHT is used as a distance measurement between reference templates and unknown utterances in the DTW algorithm. The recognition accuracy is approximately 79.25 percent using 20 speakers in each training and testing set. For the usage of the DHT in this research work, the details on this technique is described in the previous section. After the speech feature value is computed, the reference templates are created from the speech training set as shown in (20) where Ri, Rij, J are the ith reference template, the training template at the ith template of the jth training set, and J training sets respectively.  EMBED Equation.2  (20) The other research work employs this technique in conjunction with the Spectrum Distance Measurement to recognize the isolated Thai vowels and for tonal discrimination of Thai vowels. (Phatrapornnant and Jitapunkul, 1995) Two sets of Thai vowels comprise 24 Thai vowels and the other set of 3 vowels in 5 Thai tones for tonal discrimination. The 24 Thai vowels were recorded triple from 15 male speakers for total of 1,080 vowel utterances. The other 3 Thai vowels in 5 tonal levels were recorded twice from 10 male and female speakers for total of 150 vowel utterances. The average recognition accuracy of both sets is 86.11 percent and 81.00 percent respectively. The Dynamic Time Warping algorithm is one of a Dynamic Programming (DP) method. The DTW is the processing of nonlinear expansion or contraction of an unknown speech waveform to match the reference templates. Assuming two time sequences of the feature vector A and B as shown in (21). The matching distance between each template is shown in (22) where d(i,j) is the distance point at ith A-frame and jth B-frame, ain is a ith feature vector in A, bjn is a jth feature vector in B, and K is the number of feature vector. The reference template that gives the minimum distance is the recognized word in the recognition process.  EMBED Equation.2  (21)  EMBED Equation.2  (22) 4.2 Hidden Markov Model The Hidden Markov Model (HMM) technique has been widely used and employed in many speech recognition engines. This technique has been adapted to Thai speech recognition. (Areepongsa and Jitapunkul, 1995; Ahkuputra and Jitapunkul, 1997) Two research works utilize the Discreate Hidden Markov Model (DHMM) with the Vector Quantization (VQ) technique. The first research work is the recognition of isolated Thai numerals using 64 codebook vectors of 10-order LP coefficients. (Areepongsa and Jitapunkul, 1995) The speech sets are recorded twice at 8 bits and 8 KHz sampling rate from 30 male and female speakers for total of 600 utterances used in training and testing. The constrainted serial model of 3-state HMM is used in this work as shown in Figure 3. The recognition accuracy is approximately 82 percent. The second research work using the DHMM is the speaker-independent Thai connected-word recognition of Thai polysyllabic word. (Ahkuputra and Jitapunkul, 1997) This research work employs the left-right DHMM as shown in Figure 4. The experiment is conducted on the effect of varying number of model parameters--number of model states, number of codebook vectors, and number of training speakers--on the recognition accuracy. The number of model states has been set to 5, 10, 15, 20, and 25 states and the number of codebook has been set to 128 or 256 codebook vectors. The 70-word vocabulary in four sets comprising single, double, and triple syllables words, 20 words in each set, and the last set consists of ten Thai numerals from zero to nine. The speech utterances were recorded twice at 16-bit and 11.025 KHz sampling rate from 60 male and female speakers for total of 8,400 utterances. The energy level contour technique is applied in the endpoint detection analysis for speech segmentation. The 10-order LP coefficients speech features are vector-quantized by 128 or 256 referenced codebook vectors obtained from the K-Means Clustering Algorithm using Mean-Squared Error (MSE). On the HMM training procedure, the Forward-Backward procedure and the Baum-Welch reestimation procedure were implemented respectively. On the HMM testing procedure, the Viterbi algorithm is applied. The average recognition accurary is 89.906 percent using 256-vector codebooks and 15-state HMM. The recognition accuracy of each vocabulary set are 86.750 percent for single-syllabled words, 92.375 percent for double-syllabled words, 86.250 percent for triple-syllabled words, and 84.250 percent for the numeric words respectively. The state transition probability coefficient aij as shown in (23) is the model as shown in Figure 3.  EMBED Equation.2  (23)  EMBED Visio.Drawing.4  Figure 3. Constrained Serial HMM used in the Isolated Thai Numerals Recognition EMBED Visio.Drawing.4  Figure 4. Left-Right HMM used in the Thai Polysyllabic Word Recognition.The elements that characterized the Hidden Markov Model consists of state transition probability distribution matrix A with state transition coefficient aij, the observation symbol probability distribution matrix B with observation symbol coefficient bj(k), and initial state probability matrix ( with initial state probability coefficient (i as follows. (Rabiner, 1993)  EMBED Equation.3  (24)  EMBED Equation.3  (25)  EMBED Equation.3  (26) For the left-right model, the state sequence always begin at the first state and end at the last state then the initial state probability matrix will be  EMBED Equation.3  (27) From the above elements, the compact notation  EMBED Equation.3  is used to represent a Hidden Markov Model [16]. On the Hidden Markov Model implementation, three basic problems must be solved. The first problem is to find the method to compute the observation sequence probability,  EMBED Equation.3  , given the model  EMBED Equation.3  and the observation sequence  EMBED Equation.3 . The second problem is to select a corresponding state sequence  EMBED Equation.3  which is optimal to the observation  EMBED Equation.3  and the given model  EMBED Equation.3 . The third problem is to adjust the model parameters  EMBED Equation.3  in order to maximize the  EMBED Equation.3 . On training procedure, the first and the third problem are applied using the Forward-Backward Procedure and Baum-Welch Reestimation Procedure respectively. The input speech data to the model have been vector-quantized using the previously trained codebook value. The model parameters A and B are randomly initialized under the stochastic constraints as follows.  EMBED Equation.3  (28)  EMBED Equation.3  (29)  EMBED Equation.3  (30) The Forward-Backward Procedure (Rabiner, 1993) has been proposed for solving the first problem of HMM. On the forward variable (t(i) as defined in (31), the (t(i) can be solved as shown in (32)-(34) as follows.  EMBED Equation.3  (31) Forward Procedure (1) - Initialization  EMBED Equation.3  (32) Forward Procedure (2) - Induction  EMBED Equation.3  (33) Forward Procedure (3) - Termination  EMBED Equation.3  (34) As in the similar manner as the Forward Procedure, the backward variable (t(i) as defined in (35) can be solved as shown in (36)-(37) as follows.  EMBED Equation.3  (35) Backward Procedure (1) - Initialization  EMBED Equation.3  (36) Backward Procedure (2) - Induction  EMBED Equation.3  (37) The Baum-Welch Reestimation procedure (Rabiner, 1993) has been proposed to solve the third problem of HMM. The purpose of this procedure is to estimate and reestimate the HMM parameters. Let (t(i,j) as shown in (38) is the probability of being in state Si at time t and state Sj at time t+1, given the model and the observation sequence. The reestimated model  EMBED Equation.3  is shown in (39).  EMBED Equation.3  (38)  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  (39) On testing procedure, the second problem is applied using the Viterbi Algorithm. The model parameters A and B are obtained from training procedure which represent each word in the vocabulary set. The vector-quantized input speech data is then processed with parameter sets of all words that correspond to the number of syllables of each word from the endpoint detection algorithm. The output of the Viterbi Algorithm is a probability value and the optimal state sequence of each word being tested with the reference templates. The reference templates that gives the highest probability value is the recognized word to the tested word. A model parameter of a word that yields the highest probability value is the most resemblance word to the tested input speech data which is the recognized word. The Viterbi Algorithm that have been adapted to use with the Discrete Hidden Markov Model can be stated in steps as follows. (1) Initialization Step  EMBED Equation.3  (40) (2) Recursion Step  EMBED Equation.3  (41) (3) Termination Step  EMBED Equation.3  (42) (4) State Sequence Backtracking Step  EMBED Equation.3  (43) 4.3 Neural Network and Fuzzy Logic The neural network (Pornsukchandra and Jitapunkul, 1996) and fuzzy-neural network (Wutiwiwatchai, 1997) have been studied currently on speaker independent Thai numerals recognition and Thai connected word recognition. Modification of the backpropagation algorithm has also been studied presently on Thai isolated-word and connected word recognition The research work on backpropagation neural network to speaker-independent isolated Thai numerals recognition has also been conducted. The multi-layer perceptron neural network was selected using the error backpropagation algorithm in training. The neural network has 330 input nodes with one 90-node hidden layer and 10 output nodes. The 10-order LP coefficients were used in speech feature extraction. The speech utterances were recorded twice at 8 bits and 8 KHz sampling rate from 30 male and female speakers for total of 600 utterances for training and testing. The input speech samples must be time-normalized to fit the input nodes of the network. The average recognition accuracy is 73.03 percent for ten Thai numeric pronunciation from zero to nine. Currently, the fuzzy-neural network technique has also been studied on speaker-independent Thai Numerals recognition. (Wutiwiwatchai, 1997) The LP coefficient vectors are converted into the fuzzy membership vector through the modified trapeziodal fuzzy membership function. Then the fuzzy membership vectors are passed to the conventional neural network with one 100-node hidden layer and 10-node output layer. The modified class membership output value has been used in replacement of the regular class membership value. The recognition model of this fuzzy-neural network approach is shown in Figure 5. The recognition accuracy is approximately 78.30 percent using fuzzy-neural network compared to 73.30 percent using conventional neural network.  EMBED Visio.Drawing.4  Figure 5. Neural Network configuration. EMBED Visio.Drawing.4  Figure 6. Fuzzy-Neural Network Processing Diagram. EMBED Visio.Drawing.4  Figure 7. Trapezoidal Fuzzy Membership Function The Fuzzy technique in cooperation with the Neural Network has been applied to recognize the speaker-independent Thai numerals recognition. (Wutiwiwatchai, 1997) compared to the conventional multilayer perceptron neural network. From the fuzzy set theory, a pattern r subset of the universe R has been created due to the grade of membership with the membership function (A(r) to a fuzzy set A as shown in (44). The modified overlapping trapezoidal fuzzy membership functions as shown in Figure 7 have been functioned to convert a 10-order LP feature vector into a 30-order fuzzy membership feature vector as shown in (45) and then pass to the neural network inputs. The class membership function has been modified to have the output value within the range of zero to one, [0,1], which indicates the degree of similarity to that class. The process of training and testing using fuzzy-neural network is shown in Figure 6 where the class membership function has been employed in the fuzzy feature measurement and fuzzy output vector.  EMBED Equation.3  (44)  EMBED Equation.3  (45) 4.4 Modified Backpropagation Neural Network The Modified Error Backpropagation Neural Network has been proposed and applied to the Thai numeral recognition. (Maneenoi et.al., 1997) The classical error backpropagation algorithm has been modified to improve the slowness of convergence and the recognition accuracy of a conventional neural network. The modifications have been made on the slope adaptation of the activation function and the momentum weighting adjustment parameter has been added. The sigmoid activation function used in the neural network is shown in (46). The slope ( of the activation function has been modified to be adaptive to the error during training. The updating scheme of the activation function is shown in (47) and (48) using the gradient descent method. The (( is the momentum adjustment parameter for (, then, the momentum adjustment parameter for weight updating has been added as shown in the last term of (49). This will help the updated weight value not to be in a local minima and could lead to the local optimum value.  EMBED Equation.3  (46)  EMBED Equation.3  (47)  EMBED Equation.3  (48)  EMBED Equation.3  (49) 5. Future Research Directions The future research directions on Thai speech recognition and the speech analysis of Thai language will be conducted simultaneously in order to incorporate the linguistic information of the Thai language into the speech recognition system. As well as the studies on speech recognition techniques for Thai language such as the Continuous Density Hidden Markov Model (CDHMM), Semi-Continuous Density Hidden Markov Model (SCHMM), the Hybrid HMM-Neural Network, for instance. The word segmentation algorithm and the endpoint detection algorithm has been studied currently to create the robust speech segmentation technique for Thai utterances. Also, the use of Cepstral Analysis and Delta Cepstral Analysis have already been embedded into the speech feature extraction scheme in cooperation with the existing Linear Prediction analysis in the next-generation speech recognition system. The collection of various Thai utterances for Thai speech processing researches has being collected in order to set up the nation-wide standard on testing and comparison of different studies. The linguistic information of Thai language will be incorporated into the recognition system progressively with the vocabulary databases. Number of Thai vocabularies will be added up to medium or large vocabulary on the existing isolated-word and connected-word databases. Specific applications of small-vocabulary Thai speech recognition will be created such as Thai numerals recognition on telephone dialing, for instance. 6. Summary The implementation of the statistical pattern recognition model has been proved to be a proper model for speech recognition. Various recognition techniques for the pattern classification stage in the model have been modified and applied to the recognition of Thai words. Also, the development of Thai speech recognition has been presented as well as the Thai speech analysis which is the foundation of speech recognition. The research and development in this particular area is progressing to keep up with the upcoming technologies with realistic applications in the near future. 7. Acknowledgement The authors would like to acknowledge the Digital Signal Processing Research Laboratory, the Linguistic Research Unit and the Telecommunication Consortium Scholarship of the National Science and Technology Development Agancy (NSTDA) on the support of these researches. 8. References Ahkuputra, V., Jitapunkul, S., Pornsukchandra, W., and Luksaneeyanawin, S. (1997). A Speaker-Independent Thai Polysyllabic Word Recognition Using Hidden Markov Model. Proceedings of the 1997 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM97), (pp. 593-599). Areepongsa, S. and Jitapunkul, S. (1995). Speaker Independent Thai Numeral Speech Recognition by Hidden Markov Model and Vector Quantization. Proceedings of the International Symposium on Natural Language Processing, (pp. 370-378). Furui, S. (1985). Digital Speech Processing, Synthesis, and Recognition. Tokai University Press. Luksaneeyanawin, S. (1993). Linguistics Research and Thai Speech Technology. Proceedings of the International Conference on Thai Studies, School of Oriental and African Studies, University of London, United Kingdom. Maneenoi, E., Jitapunkul, S., Wutiwuwatchai, C., and Ahkuputra, V. (1997). Modification of BP Algorithm for Thai Speech Recognition. Proceedings of the International Symposium on Natural Language Processing (NLPRS97). O'Shaughnessy, D. (1988) Linear Predictive Coding. IEEE Potentials (pp. 29-32). Pensiri, R. and Jitapunkul, S. (1995). Speaker-Independent Thai Numerical Voice Recognition by using Dynamic Time Warping. Proceedings of the 18th Electrical Engineering Conference, (pp. 977-981). Phatrapornnant, T. and Jitapunkul, S. (1995). Speaker-Independent Isolated Thai Spoken Vowel Recognition by using Spectrum Distance Measurement and Dynamic Time Warping. Proceedings of the 18th Electrical Engineering Conference, (pp. 988-993). Pornsukchandra, W. and Jitapunkul, S. (1996). Speaker-Independent Thai Numeral Speech Recognition using LPC and the Back Propagation Neural Network. Proceedings of the 19th Electrical Engineering Conference, (pp. 977-981). Prathumthan, T. (1986) Thai Speech Recognition using Syllable Units. Masters thesis, Chulalongkorn University. Rabiner, L.R. (1993) A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE (pp. 257-286). Rabiner, L.R. and Juang, B.H. (1993). Fundamentals of Speech Recognition. Prentice-Hall. Rabiner, L.R. and Schafer, R.W. (1978). Digital Signal Processing of Speech Signals. Prentice-Hall. Thamphothong, P. (1990) Multispeaker Speech Recognition System. Masters Thesis, Chulalongkorn University. Thubthong, N. (1995) A Thai Speech Recognition System based on Phonemic Distinctive Features. Masters Thesis, Chulalongkorn University. Wutiwiwatchai, C. (1997). Speaker Independent Thai Numeral Speech Recognition Using Neural Network and Fuzzy Technique. Masters Thesis, Chulalongkorn University. Table 1. Summary of Current Speaker-Independent Thai Speech Recognition System Development. Speech Recognition TechniquesSpeech Feature Extraction MethodsSpeech CategoryNumber of VocabulariesTraining Set Accuracy 1Untraining Set Accuracy 2Testing Set Accuracy 3Dynamic Time Warping and Discrete Hartley Transform [1]Normalized DHT ParametersIsolated Thai Numerals1090.50 %86.50 %79.25 %Dynamic Time Warping and Spectrum Distance [2]FFT and Log EnergyIsolated Thai Vowels Isolated Thai Tonal Vowels24 15- -- -86.11 % 81.00 %3-state Discrete Hidden Markov Model [3]10 LP Coefficients 64-vector codebookIsolated Thai Numerals1097.3 %88.3 %82.00 %5, 10, 15, 20, and 25 States Discrete HMM [4]10 LP Coefficients 128 and 256 vectors codebookThai Polysyllabic Words : Single-Syllabled Words Double-Syllabled Words Triple-Syllabled Words Thai Numerals70 20 20 20 10100 % 100 % 100 % 100 % 100 %95.000 % 92.143 % 98.095 % 98.810 % 90.952 %89.906 % 86.750 % 92.375 % 96.250 % 84.250 %Neural Network [5]10 LP CoefficientsIsolated Thai Numerals1096.17 %81.00 %73.03 %Fuzzy-Neural Network [10]10 LP CoefficientsIsolated Thai Numerals10100 %77.30 %73.30 %Speech Analysis TechniquesSyllable Units Segmentation and Recognition [6]PARCOR LP Coefficients, SIFT 4, F0, Energy, DurationThai Continuous Speech Thai Numerals-93.37 % 96.87 %--Multispeakers [7]KNN / Zero CrossingIsolated Thai Words-85.80 %--Phonemic Distinctive Features [8]Tonal - F0 Height and F0 Duration Vowel - F1, F2, Duration Consonant - Zero Crossing, Noise, Duration, Min/Max/Average Energy, F2 Trans, Plosive DurationIsolated Thai Words-Tonal 97 % Vowel 100 % Consonant 99%-- Remarks : 1. Training Set is the set of speech utterances used in training process 2. Untraining Set is the set of second utterances of the same speakers but not included in the training process. 3. Testing Set is the set of speech utterances of another speakers other than those used in training. 4. Simplified Inverse Filter Tracking (SIFT)  EMBED Visio.Drawing.4  Figure 8. Various Recognition Approaches on Thai Speech Recognition Model  EMBED Visio.Drawing.4  Figure 9. Thai Speech Recognition Model using Hidden Markov Model Technique. Table 3. List of 70 Polysyllabic Words Vocabulary including Thai Numerals, Thai Single Syllable Words, Thai Double Syllables Words, and Thai Triple Syllables Words Thai Numerals<  2  3     a k|   y c p + f  P @Z &  U% } j4 ,. T/'& V^+6H (One) / hnvng1/, *- (Two) / s@@ng4/, *2! (Three) / saam4/, *5H (Four) / sii1/, +I2 (Five) / haa2/, + (Six) / hok1/, @G (Seven) / cet1/, A (Eight) / pxxt1/, @I2 (Nine) / kaw2/, (9"L (Zero) / suun4/ Single Syllable Words@4 (Walk) / dqqn0/, '4H (Run) / wing2/, - (Sleep) / n@@n0/, 2 (Eye) / taa0/, 2 (Mouth) / paak1/, +9 (Ear) / huu4/, !7- (Hand) / mvv0/, @5" (Candle) / thiian0/, 4 (Eat) / kin0/,  (Bird) / nok3/, @G (Duck) / pet1/, DH (Chicken) / kaj1/, %I'" (Banana) / kluuaj2/, *I! (Orange) / som2/, BJ0 (Table) / to3/, @*7- (Tiger) / svva4/, @5" (Bed) / tiiang0/, 1H (Sit) / nang2/, AI' (Glass) / kxxw2/, I3 (Water) / nam3/ Double Syllables Words#0B (Jump) /kra1  doot1/, +1 I2" (Turn Left) / han4  saaj3/, +1'2 (Turn Right) / han4  khwaa4/, !7- I2" (Left Hand) / mvv0  saaj3/, !7-'2 (Right Hand) / mvv0  khwaa4/, 2 I2" (Left Leg) / khaa4  saaj3/, 2'2 (Right Leg) / khaa4  khwaa4/, +1'C (Heart) / huaa4  caj0/, 22 (Pen) / paak0  kaa0/, "2% (Eraser) / jaang0  lop3/, 4*- (Pencil) / din0  s@@4/, +%-D (Lamp) / l@@t1  faj0/, -D!I (Flower) / d@@t1 maaj3/, ID!I (Tree) / ton2  maaj3/, +I2H2 (Window) /naa2  taang1/, AB! (Water Melon) / txxng0  moo0/, '11#L (Monday) /wan0  can0/, '1(8#L (Friday) /wan0  suk1/, '1@*2#L (Saturday) /wan0  saw4/, '18 (Wednesday) /wan0  phut3/ Triple Syllables Words 2)2D" (Thai) / pa0 sa0  thaj0/, D!I##1 (Ruler) / maaj3 ban0  that3/, -8+%2 (Rose) / d@@t1 ku1  lap1/, 2,42 (Clock) / naa0 li3  kaa0/, !0%0- (Papaya) / ma3 la3  k@@0/, *10# (Pineapple) / sap1 pa1 rot3/, %I'"I3'I2 (Banana) / kluuaj2 nam3  waa4/, ###8 (Truck) / rot3 ban0  thuk3/, ##00 (Mini truck) / rot3 kra1  ba1/, '1-24"L (Sunday) / wan0 ?aa0  thit3/, '1-12# (Tuesday) / wan0 ?ang0  khann0/, +1*7-@#5" (Book) /naang4  svv4  riian0/, 4B%#1! 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((InternalyB*O Referencepz & F hh>T[]@@ Publication{@d8xCJ0O0Equation | (# O TableCaptionp} & Fxx>T8h?????<O<Title1~$xx5CJItemt & F h>Th66Reference HeadingNumItem| & F h h>T:O": Affiliation CJOJQJ>O2>AbstractHeading$5CJBHead1s & Fh@& >Th? h<YR< Document Map-D  OJQJkH(U@a( Hyperlink>*B*Qu,*,W,            RH&h.<^MU]QfqNQ>t&1   )* Vst-./8P ` u89Z1~""p"""""""""""""""""""####### #,#-#/#;#<#?#K#L#O#[#\#_#k#l#o#{#|########e&&))+..S14?466j88<P?BBFEJLM^M,ORTuUUUBVV:WYG]]]],^O^_beeQffjjlhoorguruwwxxzz[{5|}b}'~jS"NQRS΃/Iab˄΄քބ)Y_cgwxDžޅ&VÆ҆JK^qч !"#$<#<#$<#$<#$<#$<#$<#$<#$<#$<#$<#$<#$<#$<#$<#!<#$<#!<#!!!<#!<#$<#! <#!<#$<#!<#PS<#!<#PS<#!<#!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!!\!!<#!<#!<#PS<#!<#PS<#!<#!<#PS<#!<#!<#PS<#!<#$<#!<#PS <#!<#!<#!<#PS<#!<#!<#!\!\!<#!<#!<#!<#!<#!<#!<#!<#!<#!<#! <#!<#!<#!<#!<#!<#PS<#!<#!<#!!!<#! <#!<#PS<#!<#!<#$ <#!<#!<#$<#!<#$<#!<#$<#!<#!<#!<#!<#!<#!<#!<#!<#!<#!<#!<#!<#!<#!<#!<#!<#!3!3!3!, !, !!!!!l!m, !, !!!!!l!hC, !, !!!!!l!hC, !, !!!!!l!hC, !, !!!!!l! , !, !!!!!l!!, !, !!!!!l!!, !, !!!!!l!!, !)Vs-v7891 !""p"~""""""""""""""""""""####### #,#-#/#;#<#?#K#L#O#[#\#_#k#l#o#{#|########+&H&e&&T)q))))))z++++.,.J.h...34?4<<P?AABBFEJiLLLLM]M^MNNO,OOOR)TGTeTTWUuUUUUU$VBVVVW:W_W}WY0YYG]a]]]]]]^,^O^_beeee3f4fQffjjjjno,oJohoruwwxxzz[{5|}b}'~jS"NOPQRS΃/Iab˄΄քބ)Y_cgwxDžޅ&VÆ҆JK^qч !"#$TˆĈň׈ 1ˉ߉ tu݋HIB؍ٍڍ3o<ƏRސXߑ!efgnx~ɒZԓ(TՔ~P P P P P P 9~|~|~|~|||||e&|e&|e&|e&|e&|e&|)|)|))|)|)|)|)|.|j8j8j8|j8|j86BBB|BBBBBBB|B|B|BB|BBB|B|B|BB|BB|BB|BB|BB|BB|BB|BB|B|BBB|BB|BB|BB|B6,^,^,^,^,^,^,^,^,^,^|,^|,^6|j|j|j|jguwzxzxzxzxzxzxzxzxzxzxzxzxzxzxzxzxzxzx`zx}x}x}xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx`xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx%,/d2ERJUGX?Z]|aRj3sy..kouvwz{|~?&&O'':/X1bsU҈{O!Ɍ:`..lnpqsty}'C8Ys‹hmrxv!!!!""""",&@&B&I&]&_&U)i)k)r)))))))))))){+++++++++.#.%.-.A.C.K._.a.i.}..444<<<AAAAAAjL~LLLLLLMMNNNNOOO#O%OOOOP%P'PQQQ/QCQEQdQxQzQQQQQ RR%R9R;RsRRRRRR*T>T@THT\T^TfTzT|TXUlUnUUUUUUU%V9V;VVVVW1W3W`WtWvWXXXY'Y)Y1YEYGYOYcYeYmYYYYYYb]v]x]]]]]]]^#^%^eeeeee4fMfOfjjjjjjnooo#o%o-oAoCoKo_oaou݋:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::8@0( >m00 B S  ?S|`|Áρہ/9ň҈isŔʔ BCCD c7c5|Visarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docVisarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docVisarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docVisarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docVisarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docVisarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docVisarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docVisarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docVisarut AhkuputraD:\Speech Recognition Development\Speech Recognition Documents\Conference Paper Documents\1997 - WORKSHOP 1997\International Workshop Paper - Thai Automatic Speech Recognition Models.docml$Sihir:OOPCON-Suda-Somchai (ml rev 1){$A =^Z=0Fc_W\_C $A =e0!_'!;M-$A =3.$A =W/$A =34$A =7:Ը?iC_2$K$A =pL$A =HU Q$A =x\$A =*@[]@hh[]@h56?????@h56?????@[]@h56?????@P[]@[]@[]@[]@[]@hh[]@h56?????@[]@[]@[]@[]^Z=W\c?iC'!ee0!7:;M-2$K3.x\pL34HU QC {W/e@ OJQJo( @`|`|Нe`|`|5(X] % . ##'',,&C.CJDMDDDtHwHJJ\\aaccvvxxA,A,A,A,@X@A,@ @A,@" @A,@T=@A"-@A@A4-AfH@AF-@I@AZ-@O@Ap-@W@A-@F`@A-Af@A-A@A-@@A-@@A-@@A-@j@A-@@A-@L@A.@@A .@b@@@@@@@@@f@d@f GTimes New Roman5Symbol3 Arial=& Cordia New;& CordiaUPC?DilleniaUPC?1MCourier Newa Book AntiquaTimes New Roman5& Tahoma"Ahh/,*&A,*&% m{ ? !0dTitle Alex Aceroml_Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Z__Zlanalysis, whichAgency c hjbjbSS 011]@"@"@"l"l"l"4# OOOO&P1;pHQ&,V,V,V,VWWWmmmmmmm,rwtLml"WWWWWm  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~W@"@",V,VQWWWW|@",Vl",Vm"&#@"@"@"@"WmWW}fk^"l"|m P<ӏ>1OW:Rm*THAI AUTOMATIC SPEECH RECOGNITION MODELS Somchai Jitapunkul, Visarut Ahkuputra, Chai Wutiwiwatchai, Nutthacha Jittiwarangkul, Ekkarit Maneenoi, Sawit Kasuriya, Pakapong Amornkul Digital Signal Processing Research Laboratory, Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, THAILAND e-mail : jsomchai@chula.ac.th Sudaporn Luksaneeyanawin Linguistic Research Unit, Department of Linguistics, Faculty of Arts, Chulalongkorn University, Bangkok 10330, THAILAND e-mail : sudaporn@chulkn.car.chula.ac.th Abstract From the pattern recognition point of view, the model of speech recognition is based on the statistical pattern recognition model that has been used widely in many speech recognition systems. The model has been modified and adapted to specific speech recognition tasks. The statistical pattern recognition model comprises three stages namely, the feature measurement stage, the pattern classification stage, and the decision rule stage. There are many techniques that have been proposed and applied to the three stages, for instance, the linear predictive coding, the Hidden Markov Model, and the Viterbi algorithm, respectively. On the feature measurement stage, there are many feature extraction techniques that have been applied to Thai language such as the linear prediction coefficient, the Fourier transform, Cepstral Analysis, etc. On the pattern classification and decision rule stages, the number of recognition techniques have been implemented on Thai speech recognition system, for example, the Hidden Markov Model, the Neural Network, the Fuzzy-Neural Network, etc. Various recognition approaches have been applied to the speaker-independent Thai speech recognition systems on isolated Thai numerals, isolated Thai words, and connected or polysyllabic Thai words. The recognition results on ten isolated Thai numerals using the Hidden Markov Model, the neural network, the modified neural network, and the fuzzy-neural network are 84.250, 73.03, 78.00, and 73.30 percent respectively. The recognition results on 70 Thai polysyllabic words using the Hidden Markov Model and vector quantization are 86.750 percent for single-syllabled words, 92.375 percent for double-syllabled words, 96.250 percent for triple-syllabled words, and 84.250 percent for numerals. Moreover, the recent advances in speech processing development on Thai language is proposed especially in the speech analysis and speech recognition area as well as the current research status, technology implementation difficulties, and future research directions on Thai speech processing. 1. Introduction Up to the present, the speech processing technologies have been advanced considerably during the past years. There are various applications of speech recognition to computer interfaces. Since speech is the most natural way of human communication and interaction. Therefore, many researches on speech processing techniques have been conducted and applied to the English language. However, some of these techyyzMU 06\bܒ 06\d>Djn DJjnĕ$*RZ|ĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽ CJOJQJCJ5CJ j UjX$8 OJPJQJUVmH5 jmUj@$8 OJPJQJUVmH jU5>*JƓؓjj|^`bp:T "$$T0p0!$$$"$$T0p0!  ܖ6<̗ڗ `n:Dʙ:Dx2Bx›ԛFVFX&2lzΞ \jTlRdZj^`bh.. CJOJQJCJ[::2›FΜМҜ&T`$ $"$$T0p0!$$T`bdfh `bdfh.."$$T0p0!  (&P P. A!"#$% +&P 0PA .!"#$% (&P P. 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!0d Title Alex Aceroml333333ff33333333ff33ffffffffffff33fft'Titlefitl Alex Acero lexlexNormalemlm4mMicrosoft Word 8.0d@d@Nx^@ o@$Uq m{Z__Z__Z__Z ՜.+,D՜.+,L px  ' Gateway 200047?: Title Title 6> _PID_GUID'AN{5247D961-4701-11D1-83E5-00609755CDB3}__Z__Z__Z__Z__ FMicrosoft Word DocumentNB6WWord.Document.8__Z__Z__Z__Z__Z__Z__ a ,, a  a,Times New Roman  .( 7a( j( 'i (hZZ__Z_ZZ__Z_ZZ__Z_ZZ__Z_ZZ__Z___Z_ZZ__Z_ZZ__Z_ZZOh+'08DP\ht_Z__Z__Z Oh+'0|  , 8 D P\dl c ,hjbjbSS 211]@"@"@"l"l"l"4# OOOO&P1pH"Q&HVHVHVHV#W#W#Wmmmmmmm,:s.uLm8l"#W#W#W#W#WmW@"@"HVHVQWWW#W|@"HVl"HVm"&#@"@"@"@"#WmWWfk^"l"m P<>1OW"Vm*THAI AUTOMATIC SPEECH RECOGNITION MODELS Somchai Jitapunkul, Visarut Ahkuputra, Chai Wutiwiwatchai, Nutthacha Jittiwarangkul, Ekkarit Maneenoi, Sawit Kasuriya, Pakapong Amornkul Digital Signal Processing Research Laboratory, Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, THAILAND e-mail : jsomchai@chula.ac.th Sudaporn Luksaneeyanawin Linguistic Research Unit, Department of Linguistics, Faculty of Arts, Chulalongkorn University, Bangkok 10330, THAILAND e-mail : sudaporn@chulkn.car.chula.ac.th Abstract From the pattern recognition point of view, the model of speech recognition is based on the statistical pattern recognition model that has been used widely in many speech recognition systems. The model has been modified and adapted to specific speech recognition tasks. The statistical pattern recognition model comprises three stages namely, the feature measurement stage, the pattern classification stage, and the decision rule stage. There are many techniques that have been proposed and applied to the three stages, for instance, the linear predictive coding, the Hidden Markov Model, and the Viterbi algorithm, respectively. On the feature measurement stage, there are many feature extraction techniques that have been applied to Thai language such as the linear prediction coefficient, the Fourier transform, Cepstral Analysis, etc. On the pattern classification and decision rule stages, the number of recognition techniques have been implemented on Thai speech recognition system, for example, the Hidden Markov Model, the Neural Network, the Fuzzy-Neural Network, etc. Various recognition approaches have been applied to the speaker-independent Thai speech recognition systems on isolated Thai numerals, isolated Thai words, and connected or polysyllabic Thai words. The recognition results on ten isolated Thai numerals using the Hidden Markov Model, the neural network, the modified neural network, and the fuzzy-neural network are 84.250, 73.03, 78.00, and 73.30 percent respectively. The recognition results on 70 Thai polysyllabic words using the Hidden Markov Model and vector quantization are 86.750 percent for single-syllabled words, 92.375 percent for double-syllabled words, 96.250 percent for triple-syllabled words, and 84.250 percent for numerals. Moreover, the recent advances in speech processing development on Thai language is proposed especially in the speech analysis and speech recognition area as well as the current research status, technology implementation difficulties, and future research directions on Thai speech processing. 1. Introduction Up to the present, the speech processing technologies have been advanced considerably during the past years. There are various applications of speech recognition to computer interfaces. Since speech is the most natural way of human communication and interaction. Therefore, many researches on speech processing techniques have been conducted and applied to the English language. However, some of these techyyzMU 06\bܒ 06\d>Djn DJjnĕ$*RZ|ĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽĽ CJOJQJCJ5CJ j UjX$8 OJPJQJUVmH5 jmUj@$8 OJPJQJUVmH jU5>*JƓؓjj|^`bp:T "$$T0p0!$$$"$$T0p0!  ܖ6<̗ڗ `n:Dʙ:Dx2Bx›ԛFVFX&2lzΞ \jTlRdZj^`bh..0 CJOJQJCJ\::2›FΜМҜ&T`$ $"$$T0p0!$$T`bdfh `bdfh..0"$$T0p0!  (&P P. A!"#$% +&P 0PA .!"#$% (&P P. A!"#$% THAI AUTOMATIC SPEECH RECOGNITION MODELSmail:e-mailDetails of each technique areTransformTransformquantifiedoverlappingmodelingFourierDiscretekHzconstrainedkHzaccuracydata, whichkHztrapezoidalanalysis, whichAgency