CORE1240 HW3

Q1

(a)

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(b)

Level	Quantization intervals (volt)	Digital word
7	0.75 $\to$ 1	111
6	0.5 $\to$ 0.75	110
5	0.25 $\to$ 0.5	101
4	0 $\to$ 0.25	100
3	-0.25 $\to$ 0	011
2	-0.5 $\to$ -0.25	010
1	-0.75 $\to$ -0.5	001
0	-1 $\to$ -0.75	000

(c)

Sample number	Sample (time, amplitude)	Digital word
1	(0, 0.2)	100
2	(2, 0.98)	111
3	(4, 0.06)	100
4	(6, 0.71)	110
5	(8, 0.44)	101
6	(10, 0.61)	110

(d)

Bit rate = 500 \cdot 3 = 1500 bits/s

Q2

(a)

Entropy = \frac{18}{341} lo g_{2} \frac{341}{18} + \frac{120}{341} lo g_{2} \frac{341}{120} + \frac{108}{341} lo g_{2} \frac{341}{108} + \frac{66}{341} lo g_{2} \frac{341}{66} + \frac{14}{341} lo g_{2} \frac{341}{14} + \frac{15}{341} lo g_{2} \frac{341}{15} \approx 2.125505608 bits/students

Minimum amount of bits required = 341 \cdot 2.125505608 \approx 724.7974123 bits

725 bits are required.

(b)

Minimum amount of bits required = 341 \cdot 6 \cdot (\frac{\frac{341}{6}}{341}) lo g_{2} (\frac{341}{\frac{341}{6}}) = 341 \cdot 6 \cdot \frac{1}{6} \cdot lo g_{2} \frac{6}{1} \approx 881.4722127 bits

882 bits are required.