課程名稱︰數位語音處理概論
課程性質︰選修
課程教師︰李琳山
開課學院：電資學院
開課系所︰電機、資工系
考試日期（年月日）︰2011.12.14
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Digital Speech Processing, Midterm
Dec. 14, 2011, 10:20-12:10
● OPEN Printed Course PowerPoint, Course Reference, Personal Notes
● You have to use CHINESE sentences to answer all of the problems
● Total point: 115
───────────────────────────────────────
1. (10) In order to recognize L isolated words w_1, w_2, ... , w_L each with
an HMM respectively, λ_1, λ_2, ... , λ_L, it is well known that one can
use either the forward algorithm (the left) or the Viterbi algorithm
(the right),
╴ ╴ ╴
arg max P(Ｏ│λ_k) ～ arg max P(q*, Ｏ│λ_k)
k k
Explain why and discuss the difference between them.
2. (10) In training HMM models for isolated word recognition, do you think
the more number of iterations you perform, the higher recognition accuracy
you'll get? Note that it is guaranteed that the likelihood function will be
increased in each iteration. Explain your answer.
3. (30) Alice, Bob and Cindy live in city A, B, and C respectively. Alice and
Bob are both interested in only 3 activities: walking in the park,
shopping, and cleaning her/his apartment. Their choices are influenced by
the weather on a given day. Cindy has no definite information about the
weather in city A or city B, but she believes that the weather both operate
as discrete Markov chains. Cindy assumes that the weather is either "Rainy"
or "Sunny", but she cannot observe them directly, that is, they are hidden.
Cindy can see that Alice and Bob post their daily activities on blogs,
those activities are the observations. The entire systems are then two
HMMs. Cindy set the following model setting:
┌───────────────────────────────────┐
│states = 'Rainy', 'Sunny'. observations = 'walk', 'shop', 'clean' │
│ │
│start_probability = ( P(Rainy), P(Sunny) ) │
│ │
│transition_probability = { P(Rainy︱Rainy), P(Sunny︱Rainy), │
│ P(Rainy︱Sunny), P(Sunny︱Sunny) } │
│ │
│observation_probability = { P( walk︱Rainy), P( walk︱Sunny), │
│ P( shop︱Rainy), P( shop︱Sunny), │
│ P(clean︱Rainy), P(clean︱Sunny) } │
└───────────────────────────────────┘
Then Cindy uses the following training algorithm to estimate the model
parameters:
──────────────────────────────────────
// Baum-Welch iterative training
Read in the observations (daily activities on Alice's/Bob's blog)
for iter = 1 to iteration_num do
Clean all accumulators
for sample = 1 to num_of_samples do
T ← length of the sample
for t = 1 to T do
calculate α_t(Rainy) and α_t(Sunny)
calculate β_t(Rainy) and β_t(Sunny)
end for
calculate γ_t(i), ε_t(i, j) iteratively where i, j = Rainy or
Sunny
accumulate
T T-1
γ_t(i), Σγ_t(i), Σγ_t(i), Σ γ_t(i),
t=1 t=1 o_t = walk
T-1
Σ γ_t(i), Σ γ_t(i), Σ ε_t(i, j)
o_t = shop o_t = clean t=1
end for
update (A, B, π)
end for
Write out the new model
──────────────────────────────────────
Please answer the following questions:
(a) (5) Besides observations (daily activities on Alice's/Bob's blog), what
should also be read in for the algorithm to execute?
(b) (5) What is Σ γ_t(i) ? i = Rainy or Sunny
o_t = walk
Use the observation (shop, walk, clean, walk, walk, clean) to explain.
Finally Cindy gets the two models.
Alice: Bob:
┌────────────────┐ ┌────────────────┐
│start_probability = (0.6, 0.4) │ │start_probability = (0.4, 0.6) │
│ │ │ │
│transition_probability = { │ │transition_probability = { │
│ 0.5, 0.5 │ │ 0.5, 0.5 │
│ 0.5, 0.5 } │ │ 0.5, 0.5 } │
│ │ │ │
│observation_probability = { │ │observation_probability = { │
│ 0.2, 0.5 │ │ 0.1, 0.5 │
│ 0.4, 0.4 │ │ 0.4, 0.3 │
│ 0.4, 0.1 } │ │ 0.5, 0.2 } │
└────────────────┘ └────────────────┘
(c) (20) Cindy collects blog articles of Alice and Bob, but two collections
have their authors missing. Please use the above models and Viterbi
algorithm to classify:
(shop, walk) (clean, clean)
4. (10) Explain the principles and procedures of estimating the probabilities
for unseen events in Katz smoothing.
5. (20) The following are the procedures of MFCC (without derivatives)
extraction
(1) Pre-emphasis
(2) Windowing
(3) Discrete Fourier Transform
(4) Mel filter-bank processing
(5) Logarithmic operation
(6) Inverse discrete Fourier transform (IDFT)
Briefly answer the following question
(a) (10) Why do we use a window to extract MFCC parameters?
(b) (10) Why pre-emphasis is performed?
6. (10)
(a) (5) Given a discrete-valued random variable X with probability
distribution
M
{p_i = Prob(X = x_i), i = 1, 2, 3, ... , M}, Σ p_i = 1
i=1
M
Explain the meaning of H(X) = - Σ p_i [log(p_i)].
i=1
(b) (5) Explain why and how H(x) above can be used as the criterion to
split a node into two in developing a decision tree.
7. (10) What is LBG algorithm and why is it better than K-means algorithm?
8. (15) Choose ONE of the problems to answer.
┌──────┐
│8-1. HW 2-1 │
└──────┘
(a) (5) In homework 2-1, we build and train digit models, "sp model" and
"sil model". What does 'sp' and 'sil' stand for seperately? How can
they be used in digit recognition?
(b) (5) What the following means?
MU + 2 {er.state[2-9].mix}
If I add it into HHEd, will the accuracy increase? Why?
(c) (5) Write down two methods (except (b)) in HW2-1 which can increase the
accuracy of recognition and explain the reasons.
┌──────┐
│8-2. HW 2-2 │
└──────┘
(a) (5) What are the voiced/unvoiced speech signals and their time domain
waveform characteristics?
(b) (5) What are the fricative consonants and their frequency
characteristics compared with voiced signals?
(c) (5) What are the plosive consonants (or stop consonants)? Describe the
way of the plosive consonants are produced and the resultant
characteristics in signals.