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(ELEC4140)[2007](f)midterm~dli^_90959.pdf
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Midterm (of ELEC331), 6th of November, 2007

Remarks: (1) This is an open exam. (2) Do all three problems.


1. (8 pts) The arithmetic decoding process is the reverse of the encoding procedure. Now, decode the message 0.23355, given the coding model as below.



Symbol Probability

0.9

!




a 0.2
0.8

u


e 0.3
0.6

o


i 0.1
0.5

i


o 0.2
e


u 0.1
0.2

! 0.1
a






2. (6 pts) Let an image block be denoted as . Now, we wish to design a 1-bit quantizer such that the quantized pixel value NN.
}1,,1,0,{,..Njixji.

, where - the mean value of the image block, ........XxifbXxifaxjijiji,,,.
...NjijixNX1,,21

such that the resulting quantizer is optimal in the MSE criterion. Determine how the two quantization levels and are computed analytically in order to obtain this optimal quantize. (Hint: Denote the set where as , and the set where as .) a
b
..ji,
Xxji.,
.
..ji,
Xxji.,
.


3. (6 pts) In the feedback predictive codec system shown below, suppose that the quantizer (Q) introduces some quantization error, i.e., . Calculate the distortion error that is produced in the coded signal , i.e., . What conclusion can you draw based on the result you obtained? ...mmee.
mx.
?....mmxx.


+

+

mx


me


me.


Entropy Coder

Q



-







mx.






+

+

mx.


Predictor



+