Signal and Systems - Dec 2011

Electronics Engineering (Semester 5)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks. 1 (a) Determine whether following signals are energy signal or power signal? Calculate their energy of power.
(i) x(t)=A cos (2? f₀ t+0)
(ii) x[n]=[1/4]ⁿ u[n](4 marks) 1 (b) Determne whether following signals are periodic or non periodic? If periodic find fundamental period.
(i) x(t)=5 cos(4?t)+3 sin(8 ? t) <br) (ii)="" x[n]="sin[6?/7" n+1]<="" a="">

</br)></span>(4 marks) 1 (c) Check whether following systems are linear or nonlinear, Time-Invariant or Time variant, casual or non casual.
(i) y(t)=x(t).cos 100 ? t
(ii) y(n)=x(n)+n?x[n+1]
(4 marks) 1 (d) Find the fourier value X(0) and value X(?) of following :
$$x\left(z\right)=\frac{1}{1+2z^{-1}-3z^{-2}}$$(4 marks) 1 (e) Find the fourier Transform of double sided exponential signal.(4 marks) 2 (a) Determine the exponential from of fourier series representation of signal show in fig 2?1 Hence determine the trignometric from of fourier series. (10 marks) 2 (b) (i) Plot the signal with respect to time.
x(t)=u(t)-r(t-1)+2r(t-2)-r(t-3)-u(t-4)-2u(t-5)
(ii) Find the even and odd of this signal.(10 marks) 3 (a) Obtain the fourier Transform of periodic gate function of amplitude A, period To and width t as shown in fig 3?1. Plot the magnitude spectrum.

(10 marks) 3 (b) State and prove following properties of Fourier Transform.
(i) Convolution in Time domain
(ii) Different in Time domain(6 marks) 3 (c) Explain Gibb's phenomenon.(4 marks) 4 (a) An analog signal.
x_a(t)=sin[480 ?t]+3sin(720 ?t) is sampled 600 times per second
(i) Determine the Nyquist sampling rate for x_a(t).
(ii) Determine the folding frequency.
(iii) What are the frequencies, in radians, in resulting discrete time signal x(n).
(iv) If x(n) is passed through an ideal D/A converter, what is the reconstructed signal Y_a(t). ?(10 marks) 4 (b) Determine the laplace transform of the signals shown in fig 4?1 and fig 4?2.

Fig 4(1)