14. Consider an angle modulation system where the transmitted signal is given by

Question

14. Consider an angle modulation system where the transmitted signal is given by u(t) Ac cos(2nfet + 5 cos 2? 100t) a) Find the power of ult) when Ac -1 b) If u(t) represents a phase-modulated signal with kp50 rad/volt, find the c) If u(t) represents a frequency-modulated signal with k 5000 Hz/volt, what is d) Let N(t) denote the noise process in the channel, and assume that its power amplitude a of the modulating signal and the modulation index Bp. the modulating signal m(t)? spectral density SN(f)AB(f). Find the autocorrelation function RN(T) and the power Py of the noise process. e) Suppose that the received signal is y(t) ut)N(t). Find the signal to noise ratio in this channel, i.e., find the ratio of the signal power to the noise power

Explanation / Answer

a)

Power of the given signal is givrn as

A2/2

Where A is amplitude of sinuusoidal signal .

Hence , P=1/2

b)

Kp= 50 rad/s

Now we need to find the

amplitude of modulatiing signal

It is clear from the given signal that Amplitude of Modulating signal is

5

Now Bp is given as :

Kp/ Frequency of the modulating signal

Bp= 50/100 = 0.5

c)

m(t)= Ac cos(2?fct+5)

Now Ac=1

kf=500 Hz/V

m(t)=cos(2?(500)t+5)

d)

Since , it is given as the frequency for m(t) and N(t) is same

We find the phase difference and define Rn(t) as :

Rn(t)=1cos(2?fct+5t)

Power of noise signal is given as :

1/((5)2/2)^{0.5}

=0.28

e)

Signal to Noise ratio is given from part a and d as :

0.5/0.28

=1.76

e)

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