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(ELEC4140)[2010](f)midterm~dli^_77933.pdf
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Midterm (of ELEC331), 25th of October, 2010
Remarks: This is an open-note exam. Duration: 16:30 pm C 17:50 pm.
Your name: Student ID:
1. (10 pts) Given a memory-less source model of 5 symbols with the probability distribution shown as follows:
Symbol
Probability
b
e
r
t
0.1
0.4
0.2
0.3
i) Design a codebook (table) for the Huffman coding of this symbol set. Generate the bit-stream after the Huffman coding of the block of symbols {better} and find how many bits have been used.
ii) Find the small interval (both bounding values) for the arithmetic coding of the same block of symbols {better} and then find the shortest binary code for this block of symbols.
2. (10 pts) Fill in all entries in the table for the feed-forward and feed-back prediction structures (referring to Pages 4 and 5 of Chapter 4), under the following assumptions: (1) use the previous element for prediction, and (2) use x+ to do quantization at any discontinuity.
Input
Feeb-forward prediction
Feed-back prediction
m
xm
.mx
em
.me
.mx.
mx.
em
0
1
2
3
4
5
6
7
8
9
100
104
122
122
124
124
120
120
118
118
-
-
-
-
100
-
-
-
-
100
3. (8 pts) In an N-dimensional space, rotation of a plane spanned by any two axes (e.g., the i-th and j-th axes) by an angle . can be denoted as the following NN matrix:
In the meantime, the reflection of one particular axis (e.g., the i-th axis) can be denoted by another NN matrix as follows:
and P(i, j) denotes the permutation between the i-th and j-th elements.
Write the butterfly structure shown in Page 22 of the transform chapter