# RTU Previous Exam Papers BE EC 5th Semester

# Communication System Dec-2011

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**UNIT-I**

1. (a) Define tHe term system ? list down the properties of a system.

(b) Prove mathematically that the signals given are periodic. For each signal, find the fundamental period and fundamental frequency. .

(i) jr(f) = 7sin3f

(ii) x(?) = sin|8/ + 30°j

(i) x(t) = ej(st + n)

(ii) x(t) = cost + sin 2/

**OR**

(a) Consider an LTI system with input x[n] and unit impulse response h[n] specified as follows –

Calculate the convolutions of theses two signals.

(b) Explain the following terms for LTI system :

(i) Memory .

(ii) nvertibility

(i) Causality

(ii) Stability

**UNIT – II**

(a) Give the Parseval’s relation for continuous time periodic signals. If the signal is periodic with period N, find the fourier series coefficients.

(b) A continuous time period signal x(t) is real valued and has a fundamental period T=8. The non zero fourier series coefficients for x(r) are

**OR**

2. (a) Give all the properties of discrete time fourier series.

(b) Use the fourier series analysis euqation to calculate the coefficients %_{n} for the continuous time periodic signal x(t) = \ ^{U} ^{w} [-1.5, \<t<2 with fundamental frequency ^{w}q^{=k}

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**UNIT – III**

(a) Explain the time scaling and time shifting property of continous time fourier transform.

(b) Consider the fourier transform pair : Using the duality property to find the fourier transform G(jw) of the signal

**OR**

3. (a) Determine the fourier transform of –

(i) 4«j = (0.5f-^{3}»[«-3]

(ii) x[n\-e a^{1} u\n]

(b) Briefly define following terms for DTFT

(i) Frequency shifting

(ii) Multiplication

**UNIT – IV**

4. (a) Find the inverse z transform of the following function by using partial fraction expansion ;

for the following ROC :

(a) |Z|>l/2

(b) |z|<l/4

<0 \<\A<\

**OR**

(a) List down the properties of ROC for the laplace transform.

(b) State and prove the initial value and final value theorem for laplace transform.

**UNIT – V**

5. (a) The signal x (f) = sin(2rc(l00)f) was sampled with sampling frequency f (period T = 1/400 sec) to obtain a discrete time signal x[n]. What is the resulting signal x[n] ?

(b) Define the term Aliasing. Give the condition by which No-Aliasing condition can be achieved.

**OR**

(a) Explain interpolation with zero-order hold circuit.

(b) Determine the Nyquist rate for the following signals :

(i) x(f) = 1 + cos (200071:?)+sin (4000jw)