Question

Q1. A single-tone FM signal which can be expressed as, s(t) = 4, cos[2oft+ß sin(21f „t)] is applied to a square-law device with output voltage v2 related to input voltage vi by vz(t)= av (t) where a is a constant. a. Determine analytic expression of the output signal. b. Explain how such a device can be used to obtain an FM signal with a greater frequency deviation (Af) than that available at the input. Q2. The spectrum of a message signal is given as |M($)=AAC 800 where f is in Hz. The signal is sampled at a rate equal to 1 kHz using flat-top pulses, with each pulse being of unit amplitude and duration 0.5 ms. a. Compute and plot the ideal (impulse) sampled signal spectrum, |M7(5).. b. Determine and sketch the amplitude spectrum of the resulting PAM signal. c. Using an ideal reconstruction (low-pass) filter, plot the spectrum of the filter output. Explain the difference between the original message signal and filter output. How can we recover m(t) from the filter output? Note: The plots of M(S)=A6) and sinc() functions are given below for your 2W information: MO M(O) -W 0 W

Answer 1

To solve above question all you need to know before is:

To get analytic expression simply expand the expression in simple form and apply following formula

Cos(2x) = 2cos^2(x) - 1

Coefficient of sinusoidal term inside the cosine term gives us modulation index. And to find out frequency modulation use following formula:

∆f = (modulation index)*(message frequency)

Rest I have explained below ask me if any queries are there in comments

(0.1) Solution : Input Vio Square low Device → output V2A niven Input V, (t) - Slo- Ac + acin (en sme}} Ackospaket (as malytic expression of the output signal alt=? Valty a a[su a [Acconſented to sin censum (13]² -> VICa Aé com {205ct + B sin censuts} coso- =) colo :: valt) - AA(4+ cos {unset+ eß since a bonts3 ) . Coo20 I + Cole 2 2. output bei Inanlgetic Expression a A Valt - a de colorateft & Msimbasuty] + 2 eters: Earlier signal sit, an FM signal had Gollowing param- signal frequency a fom Modulation index - B Carrier sresuenayafe & freamency deviation Af) a Brton Now output signal from a sanare law device has following parameters a signal trequency a tm modulation index = 28 Carrier frequency 2fc 2 BXfm :. frequency deviation 105) = it from can easily be seen that output of square low device sives twice frequency deviation before. Hence FM signal with a greater trequency deviation (of) Combe obtained. relation then