2019 DSP Homework

2019 Fall, NTUEE, Digital Speech Processing

HW#1 Discrete Hidden Markov Model

Implementing Discrete Hidden Markov Model

Training

Given a oberservation sequence, applying Baum-Welch algorithm

• Calculate $\alpha$ (forward probabilities) and $\beta$ (backward probabilities)
• Calculate temporary variable $\epsilon$ and $\gamma$
• Update model parameters by given iteration times

$A:$ Transition probability ($N{\times}N$ matrix)
$B:$ Observation probability (emission matrix) ($1{\times}N$ matrix)
$\pi:$ State sequence($1{\times}N$ matrix)

$T:$ Observation number ($T=50$ in this case)
$N:$ State number ($N=6$ in this case)
$\alpha_t(i):$ Forward variable matrix $(T{\times}N)$
$\beta_t(i):$ Backward variable matrix $(T{\times}N)$
$\gamma_t(i):$ Temporary variable ($N{\times}T$ matrix)
$\epsilon_t(i,j):$ Temporary variable (total $T-1$, each $N{\times}N$ matrix)
Notes:
$A(i,j)={a_{ij}}:$ prob. of state $i{\rightarrow}j$
$B_{jt}={b_j(o_t)}$

Note:
Accumlate interval
$\epsilon_t(i,j): 1{\leq}t{\leq}T-1$

Utils

run_train.py: Auto run the given iterations for trainning program Usage: python3 run_train.py <iterations>
check.py: Compare the testing result with labeled data. Returns the testing accuracy.
run_iters.py: Auto run multiple iterations. (defined in the file)
run_iters_tesr.py: Auto run multiple testing procedures. (defined in the file)
check_iters.py: The function is the same with check.py but for multiple iteraitons.

HW#2-1 Automatic Speech Recognition of Mandarin Digits

HW#3 ZhuYin Decoding

ZhuYin to Big5 mapping

map

How to store Big5 characters?
Every Big5 character is 2 byte, store it in uint16_t

uint16_t ch = ((uint16_t)x << 8) | (uint16_t)(y & 0xFF);

mydisambig

Mapping 注音 character back to 中文字

Example:

讓 他 十 分 ㄏ 怕
            ↓
讓 他 十 分 害 怕

Store Big5 characters in string type.

q_{t}: state at time t

Viterbi process:

Since every Big5 character has different numbers of possible states, we need capacity-flexible array to store states.

→ Using vector array, for example:

覺 → 覺
ㄉ → 八 匕 卜 不 卞 巴 比 丙...
她 → 她
ㄉ → 丁 刀 刁 大 丹 仃 弔 斗...
ㄅ → 八 匕 卜 不 卞 巴 比 丙...
現 → 現
很 → 很
棒 → 棒

Perform Viterbi algorithm on bigram probability of each Chinese character.

Initialization

$\delta(i,j)$

Record the index of maximum probability at time t in the map.

backtracking

Find the maximum probability path

NOTE The probability derivated from LM is expressed in logrithm. Use addition instead of multiplication.

Tools

generate_lm.sh: Generate the language model from ngram-count
sep_testdata.sh: Run the word separation script separator_big5.pl on test file 110.
run_all_my.sh: Run all the test text file from 110 for mydisambig and output the results.
run_all_ref.sh: Similar to run_all_my.sh but for srilm disambig.
diff_res.sh: Run diff between my results and reference results.

Final Project

Note