SIGNALS & SYSTEMS (utu previous year question paper)

SIGNALS & SYSTEMS
B.Tech Examination
SEM-IV,2011
UTTARAKHAND TECHNICAL UNIVERSITY
utu previous year question papers

Time: 3 Hours

Total Marks: 100

Section A

Attempt any four of the following:

1. With suitable example define the periodic and non-periodic signals.
2. Differentiate between the following systems:
   (i) Static systems and dynamic systems
   (ii) Stable Systems and unstable systems.
3. Consider the system : Y(t) = sin[x(t + 2)] determine whether the system is
   (i) Linear
   (ii) Stable
   (iii) Casual
   (iv) Time invariant
   (v) Memoryless.
4. Check the following system for time invariance
   (i) Y(t) = sin [x (t)]
   (ii) Y[n] = nx[n]
5. Check the following system for stability
   (i) Y(t) = e^x(t)
   (ii) X(n) = Aⁿ u(n)
6. Determine the infinite power P^∞ and infinite energy E^∞ of the following signals:
   (i) X(t) = e^-2t u(t)
   (ii) X[n] =(1/2ⁿ)u(n)

Section B

Attempt any four of the following:

1. What is Fourier series? What are the Derichlet conditions?
2. Find the trigonometric Fourier series for the continuous time wave form shown below,
   
3. Find the output of response of the LTI system for which input signals s(t) = e^-at u(t) and h(t) =u(t).
4. Determine the convolution of the two discrete time LTI system s[n] = Aⁿ u[n], and h [n] = Bⁿ u[n], for both A = B and A≠ B.
5. Determine DTFT of a discrete time signal s[n] = Aⁿ u[n], A < 1
6. Explain the following properties of DTFT:
   (i) Scaling property
   (ii) Duality

Section C

Attempt any two of the following:

1. Discuss the magnitude and phase representation of CTFT and DTFT. Explain group delay and phase delay.
2. Determine the magnitude and phase spectrum of the following:
   (i) The output response of the low-pass RC network for the input signal s(t) = e^-t/Ԏ where Ԏ = RC
   (ii) y[n] + 1/2 y[n -1] = x[n] - x[n -1]
3. Explain the following property of CTFT and DTFT:
   (i) The multiplication property
   (ii) Parseval's relation.

Section D

Attempt any two of the following:

1. State and prove the sampling theorem. Explain Nyquist rate and Sampling rate. Find the Nyquist rate and Nyquist interval for the signal
   x(t) = cos(4000π t) cos(1000π t)
2. Explain the following properties of Laplace transform:
   (i) Initial and final value theorem
   (ii) Time differentiation and frequency differentiation
   (iii) Linearity
   (iv) Multiplication by tⁿ
3. Find the inverse Laplace transform of
   

Section E

Attempt any two of the following:

1. What do you mean by region of convergence for the z transform? Find the z transform and region of convergence of the following signals.
   (i) y[n] = (n + 1)Aⁿ u[n]
   (ii) y[n] = r cos (ωn) u[n]
2. Determine the inverse z-transform of following transfer function using contour integration
3. Find the inverse z-transform of the following S(z) by
   
   (i) Partial fraction method
   (ii) Long division method
   

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