B.TechSemester 32025-26Basic Signals SystemsBEE303
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Basic Signals Systems (BEE303) - AKTU Question Paper 2025-26

B.Tech · Semester 3 · Free PDF Download

This is the official AKTU Basic Signals Systems Previous Year Question Paper for B.Tech Semester 3, academic session 2025-26. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:B.Tech
Semester:Semester 3
Session:2025-26
University:AKTU / UPTU

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Questions Asked in 2025-26

Basic Signals Systems (BEE303) — complete question paper · 70 marks · 3 Hours

Section AAttempt all q u e s t i o n s i n b r i e f . 02 x 7 = 14
  • a
    Classify signals into energy a nd power signals. Derive the con dition for each. CO
  • b
    Determine whether the system y( t) = tꞏx(t) + x(−t) is linear a nd time invariant. CO
  • c
    Write the governing differentia l equation of a mass–spring–dam per system and identify its order. CO
  • d
    State the necessary conditions for the existence of Fourier Transform. CO
  • e
    What is aliasing? Explain its effect on signal reconstruction. CO
  • f
    State and prove the Initial Value Theorem of Laplace Transform. C O 3 K 4
  • g
    Define impulse response of a continuous-time LTI system and st ate its significance. CO
Section BAttempt any three o f t h e f o l l o w i n g : 07 x 3 = 21
  • a
    (a) A signal (i) Test whether the signal is energy or power signal (ii) Find its total energy (iii) Comment on its causality
  • b
    Explain the phenomenon of sampling with the help of frequenc y-domain interpretation and derive Nyquist criterion
  • c
    Express a periodic sawt ooth waveform with period 𝑇 as a sum of shifted ramp functions and determine its Laplace transform
  • d
    Derive the relationship betw een the transfer function and th e state matrices: 𝐻ሺ𝑠ሻ ൌ 𝐶ሺ𝑠𝐼 െ𝐴ሻିଵ𝐵൅𝐷
  • e
    Define the Region of Convergen ce (ROC) for Z-transforms. Exp lain how the ROC determines the causality and stability of a discrete-time system
Section CAttempt any one p a r t o f t h e f o l l o w i n g : 07 x 1 = 07
  • a
    Derive the differential equations of motion and construct th e equivalent Force-Current(Mobility) and Force- Voltage(Impedance) electrical circuits
  • b
    A second-order system is described by If the system is critically damped ( 𝜁ൌ1 ), derive the general time-domain solution for a ramp input 𝑓ሺ𝑡ሻ ൌ𝑡⋅𝑢 ሺ𝑡ሻusing the classical method of undetermined coefficients
  • a
    A non-periodic pulse 𝑣ሺ𝑡ሻ ൌ 𝑒ି௔|௧|is applied to a bridge T-network. Use the Fourier Transform propertie s (specifically Convolution and Differentiation) to determine the output voltage 𝑣௢ሺ𝑡ሻin the frequency domain. Discuss the physical significance of the "Energy Spectr al Density" of the output signal
  • b
    Mathematically justify why the Discrete-Time Fourier Series (DTFS) exists for any periodic sequence, whereas the Discrete-Time Fou rier Transform (DTFT) requires the sequence to be absolutely summabl e (∑|𝑥ሾ𝑛ሿ| ൏ ∞). How does the introduction of the Dirichlet conditions reconcile these differences in practical hardware implementations?
  • a
    Obtain the Laplace Transform of the following waveform and h ence determine its inverse Laplace Transform
  • b
    A second-order system has transfer function Determine: (i) Impulse response (ii) Stability (iii) Steady-state value of step response using Final Value Theorem
  • a
    Derive state-space representation of a series RLC circuit an d obtain the state equations by selecting appropriate state variables
  • b
    For the state model (i) Find the State Transition Matrix (ii) Determine system stability
  • a
    Find the Z-transform a nd ROC of the sequence Also determine whether the system is stable
  • b
    Solve the following differen ce equation using Z-transform method: where 𝑥ሺ𝑛ሻ ൌ 𝑢ሺ𝑛ሻand initial rest condition applies

Question text is extracted from the official AKTU question paper PDF above. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.

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