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Reg No.:_ Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIFTH SEMESTER B.TECH DEGREE EXAMINATION(R&S), DECEMBER 2019

Course Code: EE307
Course Name: SIGNALS AND SYSTEMS

Max. Marks: 100 Duration: 3 Hours
PARTA

Answer all questions, each carries5 marks. Marks
1 Define unit ramp function. Plot r(t) and x(t) = —4r(t) (5)
2 Find the unilateral Laplace transform and ROC of x(t) = ടല + ४ * u(t) (5)
3 If Fourier transform of x(t) is X(w), derive the Fourier transform of ao (5)
4 Plot a) u[m] and 0) x[n] = u[n + 2] > u[—n+ 2] (5)
5 Consider the sequence x[n] =a”, if x[n] is a causal sequence prove that the (5)

ROC of X(z) is the exterior of the circle of radius ‏,له"‎ where X(z) is the 7.
transform of x[n].

6 State and prove the linearity and time reversal properties of Z-transform (5)

7 Determine whether Fourier series representation is possible for the discrete time (5)
signals a) x[n] = 20051577 and ಶಿ) x[n] = 4८०5 ‏ہے‎ If possible find the
fundamental period and frequency

8 Find the frequency response H(w) given, + [7] = *{x[n] + x[n— 21] (5)

PART 0
Answer any two full questions, each carries10 marks.

9 a) Find whether the system y(t) = at?x(t) + btx(t — 4) is a) static b) linear c) (6)
causal and d) time invariant
b) Given x(t) = e~*‘u(t). Find the output of the system if the impulse response of (4)
the system is given by A(t) = u(t+ 3)
10 a) A 1kf resistor is connected in series with 20017 capacitor. Using Laplace (6)

transform find the voltage across the capacitor y(t) if the voltage input is

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