Problem 1 (30 points) The spectra M₁ (w) and M₂ (w) of two different message signals m, (t) and m₂ (t) are given below.

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Problem 1 30 Points The Spectra M W And M W Of Two Different Message Signals M T And M T Are Given Below 1 (43.45 KiB) Viewed 62 times

Problem 1 (30 points) The spectra M₁ (w) and M₂ (w) of two different message signals m, (t) and m₂ (t) are given below. Suppose that these two message signals are modulated using quadrature amplitude modulation (QAM), and the carrier frequency is we = 1000m rad/s. Consider the block diagram in the lecture notes for QAM modulation and demodulation. I M₂(00) M, (co) 2) 1 00 -100m -50T 50m 100m -100 TT 100T a) Sketch the QAM modulated signal spectrum DQAM (W) (label the axes carefully). b) Verify mathematically (in the frequency domain) and graphically (in the frequency domain) that m₁ (t) is obtained when we first multiply the modulated signal by cos 1000nt and then pass the product through a low-pass filter. c) Verify mathematically (in the frequency domain) and graphically (in the frequency domain) that m₂ (t) is obtained when we first multiply the modulated signal by sin 1000nt and then pass the product through a low-pass filter.