Signals & Systems

CSET3133B.Tech CSE2023-27

Mahatma Gandhi Central University, Bihar

B.Tech Computer Science & Engineering

Semester 5 Examination, 2025

Signals & Systems (CSET3133)

Faculty: Mrs. Komal KumariMaximum Marks: 95

Assessment Questions

Signals & Systems (CSET3133) - 2025

Section A (MCQ)

(MULTIPLE CHOICE QUESTIONS – 05 Marks) Attempt all questions. Each question carries 1 mark.

  • 1

    Amplitude reversal of a signal x(t)x(t) is represented by:

  • 2

    The signal x(2t+4)x(2t+4) represents:

  • 3

    For any signal x(t)x(t), the sampling property states that:

    ∫x(t)δ(t−t0) dt=\int x(t)\delta(t-t_0)\,dt =

  • 4

    Decimation in discrete-time signals refers to:

  • 5

    The sample-and-hold circuit holds the sampled value using:

Section B (Short Answer)

(Short Answer Questions - 5 Marks) Attempt ANY TWO questions out of the following. Each question carries 2.5 Marks.

  • 1

    Using the sampling property, find: ∫(3t2+2t)δ(t−2) dt\int (3t^2+2t)\delta(t-2)\,dt and ∫e−tδ(t+1) dt\int e^{-t}\delta(t+1)\,dt

  • 2

    For a signal x(t)=u(t)x(t)=u(t), find and sketch the following:

    (a) x(−t)x(-t)

    (b) x(t−2)x(t-2)

    (c) −x(t)-x(t)

    Comment on how each transformation affects the signal.

  • 3

    Given: x[n]={1,2,0,−1}x[n]=\{1,2,0,-1\} for n=0,3n=0,3 and x[n]=0x[n]=0 otherwise.

    Form the decimated-by-2 sequence: y[n]=x[2n]y[n]=x[2n]. List its non-zero values with indices.

Section C (Long Answer)

(Long Answer Questions - 10 Marks) Attempt the questions having internal choice. Each question carries 5 marks.

  • 1

    Answer any ONE of the following

    (a)

    (a) A signal is defined as:

    x(t)={2,0≤t<11,1≤t≤20,otherwisex(t)= \begin{cases} 2, & 0\leq t<1\\ 1, & 1\leq t\leq2\\ 0, & \text{otherwise} \end{cases}

    Sketch and find the transformed signals:

    a. x(−t)x(-t) b. x(t−2)x(t-2) c. x(0.5t)x(0.5t)

    (b) Comment on how each transformation (reversal, shift, scaling) affects the signal's shape and duration.

    OR

    (b)

    (a) Prove that multiplying any signal x(t)x(t) by δ(t−t0)\delta(t-t_0) gives x(t0)δ(t−t0)x(t_0)\delta(t-t_0).

    (b) Evaluate numerically:

    • ∫(5t+7)δ(t−3) dt\int(5t+7)\delta(t-3)\,dt
    • ∫(t2−4t)δ(t+2) dt\int(t^2-4t)\delta(t+2)\,dt
  • 2

    Answer any ONE of the following

    (a)

    (a) Explain with a diagram how impulse-train sampling produces a discrete-time sequence.

    (b) Explain the relation between the unit step function u(t)u(t) and the signum function sgn(t)\text{sgn}(t) with suitable expressions and sketch.

    OR

    (b)

    (a) Derive the mathematical relation between the unit step and impulse functions.

    (b) Discuss properties of the Impulse Function.

End of Question Paper