Download AKTU B-Tech 3rd Sem 2017-2018 REC303 Signal And System Question Paper

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Paper ID: 3009

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Sub Code: REC303

B.TECH

(SEM III) THEORY EXAMINATION 2017-18

SIGNAL AND SYSTEM

Time: 3 Hours

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Total Marks: 70

Note: Attempt all Sections. If require any missing data; then choose suitably.

SECTION - A

ATTEMPT ALL QUESTIONS IN BRIEF.

2 x 7 = 14

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1. a). Check the periodicity of the signals given below. Determine the fundamental time period if signal is periodic:-
   x(t) = sin(10t – 1) – sin(4t – 1)
2. b). Find the DTFT of the causal sequence x(n) = aⁿu(n); |a| < 1
3. c). Check whether the given system are Time Variant and Causal y(t) = tx(t)
4. d). State the convolution property for continuous and discrete time domain signal in z-transform.

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5. e). Determine the Laplace transform & find out ROC for x(t)=e^-4tu(t)+e^tu(t)
6. f). Draw the signal x(t)= u(t)- u(t-2).
7. g). Using final value theorem find final value of signal corresponding to Laplace transform
   X(s) = ¹/_s(s+2)(s+8)

SECTION-B

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ATTEMPT ANY THREE PARTS OF THE FOLLOWING (3*7=21)

1. a). Find and sketch the autocorrelation function R_xx(t) for x(t) = e^at u(t), a>0
2. b). Find the convolution for given sequence
   x[n]=
   1 for n=-2,0,1
   

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   0 else
   h[n]=d[n] – d[n-1] + d[n-2] – d[n-3]
3. c). Find the Fourier transform of the signals given below:-
   i) x(t) = A, |t| < T_o;
   0, |t| > T_o
   

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   ii) x (t)= e^at u (t)
   Draw the magnitude and phase response of the transformed signal.
4. d) If X(s) = ^5s-7/_(s-1)(s+2) with -2 < R{s} < -1. Find x (t)?
5. e). State and prove sampling theorem and discuss the effect of under sampling.

Q3. ATTEMPT ANY ONE PART OF THE FOLLOWING 7*1=7

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1. a). i). What is signal? Give brief classification of signals.
   ii). Prove that power of energy signal is zero over infinite time.
2. b). Plot x(t)=u(t) –r(t-1)+ 2r(t-2)-r(t-3)+u(t-4)-2u(t-5). Find the even and odd parts of this signal.

Q4. ATTEMPT ANY ONE PARTS OF THE FOLLOWING 7*1=7

1. a). Determine whether the following continuous time system y(t)= x(t) cos (100pt) is
   

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   i) static or dynamic ii) linear or nonlinear iii) shift variant or shift invariant iv) causal or noncausal v) stable or unstable.
2. b). Find energy and power of the signal
   i). x(t)=cos(t)
   ii) x(t)=Ae^tu(t),

Q5. ATTEMPT ANY ONE PART OF THE FOLLOWING 7*1=7

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1. a). An LTI system with impulse response h₁ (n)
   h₁(n) = (¹/₃)ⁿ u(n)
   is connected in parallel with another causal LTI system with impulse response h₂(n). The resulting parallel interconnection has the frequency response.
   H(e^jw) = ^-12+5e-jw/_12-7e^-jw
   find the impulse response h₂(n).

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2. b). Find the Fourier transform of the signal x(t) = e^atu(t) and plot is magnitude and phase spectrum.

Q6. ATTEMPT ANY ONE PART OF THE FOLLOWING 7*1=7

1. a). i) Show that if x₃(t)=ax₁(t)+bx₂(t) then X₃(S)=aX₁(S)+bX₂(S)
   ii) If Laplace transform of x(t) is (s+2)/(s²+4s+5). Determine Laplace transform of y(t)=x(2t-1)u(2t-1)
2. b). A causal LTI system is described by difference equation.
   

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   y(n) = y(n-1) +y(n-2) + x(n-1)
   Find the system function H(z) for this system. Plot the poles zeros of H(z) and indicate the region of convergence.

Q7. ATTEMPT ANY ONE PART OF THE FOLLOWING 7*1=7

1. a). Consider the two continuous-time sinusoidal signals
   x₁(t)=cos(20pt) and
   

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   x₂(t)=cos(100pt)
   Which are sampled at a rate f=40Hz. Find the corresponding discrete time signals.
2. b). Explain system bandwidth and rise time for low pass filter and prove that
   t_r=0.35/B

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