Midterm Test
Ryerson University
Department of Electrical and Computer Engineering ELE635 - Communication Systems - Spring 2012 Midterm Test
Student Name: Student ID: • This is a closed book in-class examination. Only a non-programmable calculator is allowed. • No questions related to the contents of the exam will be answered during the examination. • If you think the question is not clear, use your own assumption(s) and explain why. • Answer all three questions. Each question carries equal weight. • Total time allowed is 110 minutes. 1. AM signals are demodulated by a squaring device followed by a ideal low-pass filter (LPF) and a DC blocker as shown in Figure 1. The baseband message signal is denoted as m(t). (a) Determine the expressions for signals (in time domain) at points A, B, C and D in terms of m(t). (b) Assuming A >> mp , show that y(t) yields m(t). Here, A is the amplitude of the carrier signal, mp = max|m(t)|. (c) If m(t) = 2cos(2π × 100t) + sin(2π × 150t) and carrier signal 5cos(2π × 1000t), calculate the power efficiency of this transmission. (d) For the message signal in (c), what is the lower sideband signal (LSB) in time domain? (e) For the …show more content…
A signal is given as y(t) = 2 sin(2π × 10t) + 2 cos(2π × 50t). (a) Find the Nyquist sampling rate of the signal y(t). (b) If y(t) is sampled at fs = 100 Hz, find the values of the first 5 samples. (c) If you are given that ymax (t) = 4 and ymin (t) = −4, and using the uniform quantizer whose input-output characteristic is shown in Figure 1, find the quantization stepsize q, the corresponding quantization levels and the pulse code modulated (PCM) codes of the 5 samples found in part (b). (d) For the above quantizer, derive the signal-to-quantization-noise ratio (SQNR). No credit will be given if you simply use any SQNR formula. (e) Now assume that y(t) is sampled 2.5 times the Nyquist rate, and each sample is represented using 8 bits. What is the capacity of a CD (in bytes) to store the sampled signal of one hour
Department of Electrical and Computer Engineering ELE635 - Communication Systems - Spring 2012 Midterm Test
Student Name: Student ID: • This is a closed book in-class examination. Only a non-programmable calculator is allowed. • No questions related to the contents of the exam will be answered during the examination. • If you think the question is not clear, use your own assumption(s) and explain why. • Answer all three questions. Each question carries equal weight. • Total time allowed is 110 minutes. 1. AM signals are demodulated by a squaring device followed by a ideal low-pass filter (LPF) and a DC blocker as shown in Figure 1. The baseband message signal is denoted as m(t). (a) Determine the expressions for signals (in time domain) at points A, B, C and D in terms of m(t). (b) Assuming A >> mp , show that y(t) yields m(t). Here, A is the amplitude of the carrier signal, mp = max|m(t)|. (c) If m(t) = 2cos(2π × 100t) + sin(2π × 150t) and carrier signal 5cos(2π × 1000t), calculate the power efficiency of this transmission. (d) For the message signal in (c), what is the lower sideband signal (LSB) in time domain? (e) For the …show more content…
A signal is given as y(t) = 2 sin(2π × 10t) + 2 cos(2π × 50t). (a) Find the Nyquist sampling rate of the signal y(t). (b) If y(t) is sampled at fs = 100 Hz, find the values of the first 5 samples. (c) If you are given that ymax (t) = 4 and ymin (t) = −4, and using the uniform quantizer whose input-output characteristic is shown in Figure 1, find the quantization stepsize q, the corresponding quantization levels and the pulse code modulated (PCM) codes of the 5 samples found in part (b). (d) For the above quantizer, derive the signal-to-quantization-noise ratio (SQNR). No credit will be given if you simply use any SQNR formula. (e) Now assume that y(t) is sampled 2.5 times the Nyquist rate, and each sample is represented using 8 bits. What is the capacity of a CD (in bytes) to store the sampled signal of one hour