HoChiMinh City University of Technology Department of Telecommunications Engineering MIDTERM EXAMINATION Course: Communications I Date: 20/10/2014 Duration: 90 minutes IMPORTANT NOTE: One A4-size note and calculator are permitted. Question 1 (50 marks) Consider a signal and a linear system as shown in Figure 1 where x ( t )= A + cos ( 2π f 0t ) and 1 , 0 ≤ t ≤ Tp h ( t ) = Tp h(t) x(t) y(t) 0, elsewhere Figure 1: System A, f0, Tp are constants. 1) Is the system stable and causal? (10 marks) 2) Show that x(t) is periodic. Find its period. (10 marks) 3) Classify y(t) as an energy signal or a power signal. (10 marks) 4) Find the power spectral densities of the input and the output. Then based on the power spectral densities, compute the input power and the output power. (10 marks) 5) Find the autocorrelation functions of the input and the output. (10 marks) Question 2 (20 marks) Consider a commercial FM superheterodyne receiver with the intermediate frequency fIF = 10.7 MHz. The standard FM broadcast band extends from 88.1 MHz to 107.9MHz. Assume that the local oscillator is designed for low-side tuning. 1) Determine the frequency range of the local oscillator to receive all FM signals. (10 marks) 2) Find the range of image frequencies. (10 marks) Question 3 (10 marks) An AM system operates with a modulation index of 0.7, and the power in the normalized modulating signal is 0.2W. The AM signal is transmitted through a channel with the Gaussian noise. Calculate the efficiency of the AM modulator. Question 4 (10 marks) A delta modulator has the message signal m(t) = 4cos(40πt). Find the minimum sampling frequency required to avoid slope overload, assuming that the impulse weights δ0 are 0.1π. Question 5 (10 marks) An FM modulator generates a signal = xFM ( t ) 10 cos ( 2000π t + 2 sin (16π t ) ) with the frequency deviation constant fd = 8 Hz. 1) Find the unmodulated carrier signal. (5 marks) 2) Determine the modulating signal. (5 marks) -------------------------- END OF QUESTION PAPER --------------------------
