EX-302 Signals And Systems - Dec 2025 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aDescribe periodic and aperiodic signals as well as energy and power signals with neat sketch.
   How to answer

   • Define periodic signal x(t)=x(t+T) and aperiodic signal with examples
   • Define energy vs power signals with energy and power formulas
   • Give neat sketches for each type
   • Summarize comparison / classification conditions
2. 7 Marks
   bFind whether the following signals are energy or power signal or neither. (i) $x(t) = t^2u(t-1)$ (ii) $x(t) = 2u(t)-u(t-3)$
   How to answer

   • Use energy integral and average power limit formulas for CT signals
   • Evaluate (i) $x(t)=t^2u(t-1)$ for convergence of E and P
   • Evaluate (ii) $x(t)=2u(t)-u(t-3)$ finite-duration pulse
   • Classify as energy / power / neither with justification
3. 7 Marks
   aExplain even and odd signals with example and also derive the relationship between impulse and unit function.
   How to answer

   • Define even $x(-t)=x(t)$ and odd $x(-t)=-x(t)$ signals with examples and sketches
   • Define impulse $\delta(t)$ and unit step $u(t)$ functions
   • Derive $u(t)=\int_{-\infty}^{t}\delta(\tau)d\tau$ and $\delta(t)=du(t)/dt$
   • Give properties / verification
4. 7 Marks
   bDefine basic properties of signals.
   How to answer

   • Define signal and need for properties
   • List basic properties: amplitude, time scaling, shifting, reversal, periodicity etc.
   • Brief explanation of each property
   • Give mathematical expression / example
5. 7 Marks
   aDiscuss different advantages of wavelet transform on other transforms, also discuss few properties that a function need to satisfy.
   How to answer

   • Introduce wavelet vs Fourier/STFT/Laplace transforms
   • List advantages: time-frequency localization, multiresolution, transient analysis
   • State admissibility / properties a wavelet function must satisfy
   • Give examples of wavelet functions
6. 7 Marks
   bDefine Laplace transform and derive the relationship between Laplace and Fourier transform.
   How to answer

   • Define Laplace transform integral with ROC and s=sigma+jomega
   • Define Fourier transform integral
   • Show Laplace reduces to Fourier for sigma=0 / on jw-axis
   • State condition for existence and relation
7. 7 Marks
   aDetermine the Fourier series expansion for the given waveform.

   How to answer

   • Identify period $4\pi$ and amplitude $\pm A$ from waveform symmetry
   • Set up Fourier series integrals for $a_0, a_n, b_n$
   • Evaluate coefficients using even/odd symmetry
   • Write final trigonometric / exponential series
8. 7 Marks
   bProve the convolution of Laplace and write its statement.
   How to answer

   • State Laplace convolution theorem: L{x1*x2}=X1(s)X2(s)
   • Define convolution integral in time domain
   • Prove using Laplace integral and change of variables
   • Mention ROC and application
9. 7 Marks
   aWrite short notes on :

   1. i)LTI system
   2. ii)Analog filters
   How to answer

   • Define LTI system: linearity + time invariance with conditions
   • Give properties / representation via impulse response and convolution
   • Define analog filters: types LPF, HPF, BPF, BSF and purpose
   • Give example / frequency response idea
10. 7 Marks
    bDetermine the response of the system $y(n) = \frac{5}{6}y(n-1)-\frac{1}{6}y(n-2) + x(n)$ to the input signal $x(n) = \delta(n)-\frac{1}{3}\delta(n-1)$.
    How to answer

    • Take z-transform / assume zero initial conditions for difference equation
    • Find transfer function H(z) and input X(z)
    • Find Y(z)=H(z)X(z) and partial fraction expansion
    • Take inverse z-transform to get y(n)
11. 7 Marks
    aDefine impulse response, step response and frequency response.
    How to answer

    • Define impulse response h(t) as output for delta input
    • Define step response s(t) as output for u(t) and relation s = integral of h
    • Define frequency response H(jw) as Fourier transform of h
    • Give significance / example
12. 7 Marks
    bFind the convolution sum between $x(n) = \{-3,1,2,3\}$ and $h(n) = \{-2,1,0,2\}$.
    How to answer

    • Write sequences x(n)={-3,1,2,3} and h(n)={-2,1,0,2}
    • Apply convolution sum formula y(n)=sum x(k)h(n-k)
    • Compute using tabular / matrix method step by step
    • Write resulting sequence y(n) with length 7
13. 7 Marks
    aUsing properties of z-transform, find z-transform and ROC of signal $\frac{1}{(1-z^{-1})^2}$.
    How to answer

    • Recall standard pair for $1/(1-z^{-1})$ and differentiation property
    • Apply differentiation / multiplication by n property to get $1/(1-z^{-1})^2$
    • Determine ROC as |z|>1 for causal sequence
    • Write final X(z) and ROC
14. 7 Marks
    bDefine sampling and how to avoid aliasing effect in sampling.
    How to answer

    • Define sampling: conversion of CT to DT at rate fs
    • Explain Nyquist criterion fs >= 2fm
    • Explain aliasing effect with spectrum overlap diagram
    • List methods to avoid aliasing: anti-aliasing filter, higher fs
15. 7 Marks
    aExplain with suitable example what is state variable representation of an LTI CT system.
    How to answer

    • Define state, state variables, state vector for CT LTI system
    • Write state equation dx/dt=Ax+Bu and output y=Cx+Du
    • Give suitable example e.g. RLC / second-order system
    • Explain advantages of state representation
16. 7 Marks
    bIf $x(n)=\{1,5,-2,1,3,4,2,0,5\}$ then find DTFT $[x(e^{j\omega})]$.
    How to answer

    • Recall DTFT definition $X(e^{j\omega})=\sum_n x(n)e^{-j\omega n}$
    • Substitute finite sequence {1,5,-2,1,3,4,2,0,5}
    • Simplify into sum of exponential terms
    • Write final closed-form expression