SYSC3501 Communication Theory Assignment #3 Due: 4:00pm Wednesday March 15 th 2011 Question 1 Suppose a signal m(t) (shown in the figure below) is transmitted using frequency modulation. (a) Write the expression of f i (t), the instantaneous frequency, in terms of m(t) for modulated signal, where () ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = ∫ ∞ − t c d m k t f A t s λ π 2 2 cos , with f c =100Hz, A = 2 and k = 3. (b) Sketch f i (t), θ (t), the phase deviation, and the modulated signal s(t). Provide appropriate labels on the sketch x- and y-axes. (c) What is the maximum frequency deviation and maximum phase deviation for this FM signal? Question 2 Let () ) t 40 ( Sa 40 t w = . (a) Find the Fourier transform ( ) f W and sketch ( ) f W . (b) If () t w is sampled with a sampling frequency of Hz 75 f s = (we assume ideal sampling, i.e. the sampling waveform is a unit-weight impulse train), plot the magnitude
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