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ELE324hw6a - envelope iv Now generate the complex transfer...

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Due ?, 200? ELE 324 - TELECOM I HW 6 In this homework, we study demodulation of FM waves. i) Generate a modulating sinusoidal signal m(n) = cos(2 π fm n ) with (normalized) frequency fm=1/256 for n=1,2,…,256. Plot m(n). ii) Generate a Frequency Modulated wave with (normalized) carrier frequency fc=0.25 and modulating signal m(n) as: s(n) = cos(2 π fc n + 2 π kf Σ m(i)) where kf=0.1 [ integral (from 0 to t) in the continuous time is replaced by summation (from 1 to n)]. Plot s(n) and its magnitude spectrum (use abs and dft or fft commands). iii) In order to obtain the complex envelope, sc(n), of the FM wave, s(n), first use hilbert command and then shift this signal to baseband by multiplying with a signal c(n) = exp(-j2 π fc n ). Plot the magnitude spectrum of the complex
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Unformatted text preview: envelope. iv) Now generate the complex transfer function of the slope circuit: First create H(k) = j(k-128+32) for k=96,97,…,160, and H(k) = 0 elsewhere. Then use fftshift command on H to obtain the complex transfer function Hc. Plot magnitude of the complex transfer function, Hc. v) Obtain the Fourier transform, Yc, of the complex envelope yc(n) of the slope circuit response y(n) to the input FM signal by multiplying the Fourier transform, Sc, of the complex envelope, sc(n), of the FM signal with the complex transfer function, Hc. Plot the magnitude spectrum of the output complex envelope. vi) Obtain the complex envelope in the time domain and find its envelope (use abs ). Plot the envelope and compare with m(n). vii) Comment on the results....
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