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EC403

USN 1

M.S. RAMATAH INSTITUTE OF TECHNOLOGY

(AUTONOMOUS INSTITUTE, AFFILIATED TO VTU)

BANGALORE - 560 054

SEMESTER END EXAMINATIONS - JUNE 2010Course & Branch : BE (Electronics and Communication) Se mester IV

Subject Signals and Systems M a x. Marks : 100

Subject Code : EC403 Du ration : 3 hr

Instructions to the Candidates:

Answer one full question from each unit.

UNIT-I

1. a) Consder the anaog sgna x(t)=3cos(2r 100 t) (06)

i) Determine the minimum sampling rate required to avoid

aliasing.

ii) Suppose that the signal is sampled at the rate F5=200Hz, what

is the discrete time signal obtained after sampling?

iii) Suppose the signal is sampled at the rate FS=75Hz, what is the

discrete time signal obtained after sampling?

b) Show that x(n)=xe (n)+ xo (n) (04)

c) Adscree- tmesysemcanbe(10)

i) Static ii) time invariant iii) Lineariv)- Causal v) Stable

Examine the following systems with respect to the properties above

a) y(n) = cos (x(n)) b) y(n) = Ax(n)+B2 a) Skechthefolowngsgnas(06

i) (n 2-2) [u(n) - u(n-5)] ii) (n-2)u(n-1)b) Derive an expression to show that the SQNR increases approximately by (08)

6dB for every bit added to the word length of ADC. Give the relevant

diagrams.

c) Determne the response of the following systemto the input signal (06)

IInl, -3Sn-<3z(n) =

0, otherwise

i) y(n) = x(n + l) ii) y(n) = 3 [x(n + 1) + x(n) + x(n -1)]

iii) y(n) = max[x(n +1), x(n), x(n -1)]

UNIT-II

dx(t)Show that a differe tiat r t t = i b th li i. a) n o sys em y( ) s o near an t me (05)

d t

b)invariant.

Determine the convolution of x(t) and h(t)where'x(t)=h(t)=u(t)-u(t-1). (07)

Plot y(t).

c) A LTI system has impulse response given by h(n)=u(n)-u(n-10). (08)

Determine the output of the system when the input is rectangular pulse

defined by x(n)=u(n-2)-u(n-7).

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EC403

4. a) If Hip (jw) is an ideal low pass filter with its band edge at w,o show that (06)

G(jw) = 1-Hip (jw) is an ideal high pass filter with same band edge.

b) Suppose that the impulse response of an LTI systemis (06)

c )

4

6. a)

Fig.4c

UNIT-III

b)

(08)

5. a) Find the inverse Fourier transform of X(jw= 1(a+wz(

6)

b) State and prove the time differentiation and convolution property of Fourier (07)transform.

C Fndthe Fourier transformof the folowng(07)

UNIT-IV

7. a) Derive an expression for 8 point DIF FFT and draw its signal flow graph.

(07)

-T <rSTDraw the (07)

jtj>T

spectrum.

c) State and prove the modulation and integration property of Fourier (06)

transform.

b )

x(t) =e-2t

[u(t) -u(t -2)]

h(t)=u(t-1)-u(t-2), implement this system by a combination of i) parallel

systems ii) cascade systems.

The impulse response of a RC system shown in Fig.4c is h(t)=e`u(t).

Determne the output of the systemif the input voltage is

i) x(t) co s wct ii)e-2t u(t-3)

Find the Fourier transform of the given signal x(t)=e-°̀u(t), a > 0. Draw its

magnitude and phase spectra.

Consider the rectangular pulse defined as x(t)=

Perform the circular convolution of a 4-point sequence x1(n) =2"u(n) and

x2 (n) = nu(n)

c) Show the relationship between DFT and DTFT.

8. a) Find the 4-point DFT of the sequence x(n) =cos n7r---4

b) Compute 8-point circular convolution of the following sequences in time

(10)

(07)

(03)

(08)

(12)

domain. xl(n)={1, 1, 1, 1, 0, 0,0,0} x2(n)=cos(2g f, 0<n57

UNITVJ

9. a) Show that the Fourier transformof a periodic impulse train modulated by (10)

x(t) is composed of periodically repeated copies of

- ( ,-zkX(jo). XS(j(O)= 1 >X j w-2

TS k= a o T,

b) Show that the DSBAM-TC modulation system is not a linear system . Show (10)

that it is riot a time - invariant system.

10 a) Wththe help of a block dagramexplainFDM (08)

b) The impulse response of an overall system is h(t)[8(t)-8(t-T)] * u(t). (06)

Evaluate and plot the response.

c) Show that amplitude modulator is linear and not time invariant system. (06)*****************

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