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Homework_1_solutions(1)

# Homework_1_solutions(1) - 1 EE113 Homework 1 Solutions...

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1 EE113 Homework 1 Solutions Problem 1.2 Consider the continuous-time signal x ( t ) = 0 . 5 sin(2 πt + π 3 ) , where t is in seconds. Plot the samples of the sequence x ( n ) that are obtained by sampling x ( t ) at multiples of T = 0 . 25 second over the interval t [0 , 3] . Solution: See the plot below. 0 0.5 1 1.5 2 2.5 3 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 t x ( t ) October 26, 2011 DRAFT

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2 Problem 1.4 Fig 1.14 (from Prob. 1.3) shows the samples of a sequence, x ( n ) , over the interval 0 n 7 . Plot the quantized version, x q ( n ) , according to the mapping of Fig. 1.5 and assuming Δ = 1 / 2 . Write down the resulting bit sequence. Solution: See the plot below. October 26, 2011 DRAFT
3 0 1 2 3 4 5 6 7 8 -1 -0.5 0 0.5 1 1.5 n x q ( n ) The resulting bit sequence is 001 , 001 , 111 , 010 , 000 , 010 , 001 , 010 October 26, 2011 DRAFT

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4 Problem 1.6 Refer to the quantization procedure described in Fig. 1.5. Assume Δ = 1 / 8 . Determine the samples x q ( n ) that correspond to the following sequence of bits (assume the first sample occurs at n = 0 ): 001100110101101111100011110101001000001 How many samples are represented in this sequence of bits? How many bits would you need to represent 2048 samples of x ( n ) ? Solution: The sample sequence is 001 100 110 101 101 111 100 011 110 101 001 000 001 arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv arrowdblbothv 1 8 1 2 1 4 3 8 3 8 1 8 1 2 3 8 1 4 3 8 1 8 0 1 8 There are 13 samples represented in this sequence of bits. We need 2048
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