Problem 3 (20 points) A message signal is given as t₁ m(t)=2-t, 0st<1 1st <2 elsewhere Assume the carrier amplitude A =

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Problem 3 20 Points A Message Signal Is Given As T M T 2 T 0st 1 1st 2 Elsewhere Assume The Carrier Amplitude A 1 (37.66 KiB) Viewed 28 times

Problem 3 (20 points) A message signal is given as t₁ m(t)=2-t, 0st<1 1st <2 elsewhere Assume the carrier amplitude A = 1 and the carrier frequency fe = 1 kHz. a) If m(t) is phase-modulated with kp, write the mathematical expression of PPM(t) and sketch it. b) if m(t) is frequency-modulated with k, =#, write the mathematical expression of Pr(t) and sketch it. Problem 4 (40 points) Suppose that the message signal is m(t)=6cos 2000-2 sin 4000r, o, -10° rad/s, A-5, and k, -10'x. a) Write the expression of (1) (use the indefinite integral of m(t)). b) Calculate the bandwidth of (1). c) What should be the value of k, for r(t) to have the same bandwidth as that of 9rm (1)? d) Write the expression of ru (1) by using the k, value you have found in (c).