Download AKTU B-Tech 5th Sem 2016-2017 Computer Architecture Ncs 505 Question Paper

ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES (AUTONOMOUS)

MCA I Semester Regular Examinations November - 2015

(Approved by AICTE, Accredited by NBA & Affiliated to AU)

SIGNALS AND SYSTEMS

Date: Time: 3 hours Max Marks: 60

**Answer ONE Question from each part. All questions carry equal marks.**

PART-1

1. a) Explain the properties of the following signals

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   1. Unit impulse signal
   2. Unit step signal
   3. Ramp signal

   (6 Marks)

   b) Determine whether the following signals are periodic or not. If periodic find the fundamental period.

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   1. x(t) = 2cos(t/4) + cos(t/3)
   2. x(t) = cos²t

   (6 Marks)

2. a) Explain the properties of Fourier series.

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   (6 Marks)

   b) Obtain the Fourier series representation of the half wave rectified sine wave.

   (6 Marks)

PART-2

3. a) State and prove properties of Fourier transform.

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   (6 Marks)

   b) Find the Fourier transform of gate function.

   (6 Marks)

4. a) Explain the concept of Hilbert transform.

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   (6 Marks)

   b) Find the inverse Laplace transform of the following function:

   X(s) = (s² + 1) / (s+3)(s+2)²

   (6 Marks)

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PART-3

5. a) What is an LTI system? Explain the properties of LTI system.

   (6 Marks)

   b) Explain the difference between causality and stability of a system.

   (6 Marks)

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6. a) Explain the properties of convolution.

   (6 Marks)

   b) Find the convolution of the following signals graphically

   x(t) = e^-2tu(t); h(t) = e^-3tu(t)

   (6 Marks)

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PART-4

7. a) State and prove sampling theorem for band limited signals.

   (6 Marks)

   b) Explain the effects of under sampling.

   (6 Marks)

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8. a) Explain the concept of energy and power spectral density.

   (6 Marks)

   b) Find the auto correlation of x(t) = Au(t)

   (6 Marks)

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PART-5

9. a) Explain the properties of Z-transform.

   (6 Marks)

   b) Determine the Z-transform of the following signal

   x(n) = n²u(n)

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   (6 Marks)

10. a) Find the inverse Z-transform of

    X(z) = (3z^-1) / (1 - (3/2)z^-1 + (1/2)z^-2)

    ROC: |z| > 1

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    (6 Marks)

    b) Explain the applications of Z-transform.

    (6 Marks)

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