課程名稱︰數位語音處理概論 課程性質︰電機系/資訊系選修 課程教師︰李琳山 開課學院：電資學院 開課系所︰電機系 考試日期（年月日）︰107.11.28 考試時限（分鐘）：120 試題 : 註：部分數學式以LaTeX語法表達。 1. Take a look at the block diagram of a speech recognition system in Figure 1. https://imgur.com/undefined (a) In the block of front-end processing, why doe we use the filter-bank? (4 %) (b) Explain the rules of the acoustic models, lexicon, and language model in Figure 1? (12%) (c) Why do we need smoothing in the language model? (2%) (d) Which part includes the HMM-GMM? (2%) 2. Given a HMM \lambda = (A, B, \pi) with N states, an observation sequence \bar{O} = o_1...o_t...o_T and a state sequence \bar{q} = q_1...q_t...q_T, d- fine \alpha_t(i) = Prob[o_1...o_t, q_t = i | \lambda] \beta_t(i) = Prob[o_{t+1}...oT | q_t = i, \lambda] (a) What is \sum_{i=1}^N\alpha_t(i)\beta_t(i)? Show your results. (4%) (b) What is \frac{\alpha_T(i)\beta_t(i)}{\sum_{j=1}^N\alpha_t(j)\beta_t(j)}? Show your results. (4%) (c) What is \alpha_t(i_a_{ij}b_j(o_{t+1})\beta_{t+1}(j)? Show your results. (4%) (d) Formulate and describe the Viterbi algorithm to find the best state seq- uence \bar{q}^* = q_1^*...q_T^* giving the highest probability Prob[\bar{O}, \bar{q}^* | \lambda]. Explain how it works and why backtracki- ng is necessary. (4%) 3. Explain what is a tree lexicon and whuy it is useful in speech recognition. (8%) 4. (a) Given a discrete-valued random variable X with probability distribution {p_i = Prob(X = x_i), i = 1,...,M}. \sum_{i=1}^M = 1. Explain the meaning of H(X) = -\sum_{i=1}^M p_i[\log(p_i)]. (b) Explain why and how H(X) above can be used to select the criterion to s- plit a node into two in developing a decision tree. (4%) 5. (a) What is the perplexity of a language source? (4%) (b) What is the perplexity of a language model with respect to a corpus? (4%) (c) How are they related to a "virtual vocabulary"? (4%) 6. Please answer the following questions. (a) Explain what a triphone is and why it is useful? (4%) (b) Explain why and how the unseen triphones can be trained using decision tree. (4%) 7. What is the prosody of speech signals? How is it related to text-to-speech sunthesis of speech? (6%) 8. Explain why and how bean search and two-pass search are useful in large voc- abulary continuous speech recognition. (8%) 9. Please briefly describe LBG algorithm and K-means algorithm respectively. W- hich one of the above two algorithms usually performs better? (Explain your answer with description, not just formulate only.) (8%) 10. Homework problems (You can choose either HW2-1 or HW2-2 to answer). HW2-1 (a) We added the sp and sil model in HW@-1. How can they be used in digital recognition? (2%) (b) Write down two methods to improve the baseline of the digital recogniz- er and explain the reason. (4%) HW2-2 (a) Why do we use Right-COntext-Dependent Initial/Final to label? (2%) (b) What characteristics can we use to help distinguish the Initials and F- inals? (4%) --

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