r (Fotlowing Paper ID and Roll No. to be filled in your Answer Book) B.Tech. (sEM. IIf) THEORY EXAMINATION, 2015-1 6 BASIC SYSTBM ANAIXSN (NEE-303/EEE-301) BASrC OF SIGNALS l & SYSTEMS (EE-302) Section-A [Total Marks:1001 [Time:3 hoursl l. Attclnpts all parts. All parts carry equal marks. Write (2x10=20) answer of each part in short. (a) Define unit step and unit ramp signals with proper sketch. (b) (c) (d) (e) (0 (g) _(h) 11000 Check the periodicity of the signal x(t):sl!Ot Write Dirichlet conditions for the existence Fourier series. of Find the Fourier transform of (t-to). What is time invariant and time varying system.? State initial value theorem of z-transforrlls. Find Z-transform ofunit step and impulse functions Derive [,aplace transfoffn of sinh cot (1) . P.T.O.
(i) Express the given signal in terms of step signals. x(t) FIg.1 0) otstate space representatrou |;il:::|;il:::' Section-B Attempts any five question from this 2. (a) sectiorls. ( l0x5:50) the signal Find the even and odd components of shown in figure. '2 '1 o Flg.2 il000 (2) NEE-3 03 /EEE-3 0 I /EE- 302
(b) Draw the force-Current analogy ofthe mechanical given in figure. -r -l L k1 \\ J'''LI \ \\ B. + MT J82 M2 r(tI ) )r( No Frlclon FlSl'3 Explain the trigonometric and exponential forms of Fourier series representation of periodic signals- Find the trigonometric Fourier series for the periodic signal shoun in fizure 4. (a) 11000 State and prove duality property transfolrll. (3) of Fourier P.T.o.
(b) function Find the Fourier transform of rectangular shown in fig. theorem of laplace state and prove initial and final value 5. transfonn. apptication of Discuss the important properties and transfonn solve the Laplace transform. usin gLaplace following differerrtial equation- 6. *(o) = 0' x(o) = r 2ii(t) + 7x(t) + 6x(t) = 0; 7. 8. il Findthe Z-ttansform of following functions: (i) x[n]:anu[nJ (ii) x[n]:-bnu[-n-1] (a) prove the convolution theorem of z-ttansfonn. (b) F'ind the 7,-ttartsform of coswonuln]. 000 (4) NEE-303/EEE-301 IEE-302