EX-302 Signals and Systems - Jun 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
   aDefine Signal. Compare continuous time and discrete time signal.
   How to answer

   • Define signal as function of independent variable carrying information.
   • Define continuous-time signal with examples.
   • Define discrete-time signal with examples.
   • Compare on basis of independent variable, representation, examples.
2. 7 Marks
   bExplain the classification of signals in detail.
   How to answer

   • State need for classification of signals.
   • Explain deterministic vs random, periodic vs aperiodic, energy vs power.
   • Explain even vs odd, causal vs non-causal, continuous vs discrete.
   • Give example for each class.
3. 7 Marks
   aDetermine whether the give signals are periodic or non-periodic

   1. i)$\sin\left(\frac{\pi t}{4}\right)u(t)$
   2. ii)$\cos 15\pi t + \sin 13t$
   How to answer

   • Check periodicity condition $x(t)=x(t+T)$.
   • Analyze i) $\sin(\pi t/4)u(t)$ effect of $u(t)$ on periodicity.
   • Find periods of $\cos 15\pi t$ and $\sin 13t$ and their ratio.
   • Conclude periodic or non-periodic with fundamental period if applicable.
4. 7 Marks
   bCompare the following with example.

   1. i)Even and odd signal
   2. ii)Energy and power signal
   How to answer

   • Define even and odd signals with condition and example.
   • Define energy and power signals with formulas and example.
   • Compare properties and give graphical examples.
   • Summarize differences in tabular form.
5. 7 Marks
   aWrite down the five properties of Fourier transform. Also explain duality.
   How to answer

   • Define Fourier transform pair.
   • List five properties e.g. linearity, shifting, scaling, convolution, duality.
   • State duality property $X(t) \leftrightarrow 2\pi x(-\omega)$.
   • Explain duality with example.
6. 7 Marks
   bExplain the limitation of Fourier series. Also explain Dirichlets conditions in brief.
   How to answer

   • Define Fourier series for periodic signals.
   • Explain limitations: only periodic, convergence issues, Gibbs phenomenon.
   • State Dirichlet conditions in brief.
   • Give example where conditions fail.
7. 7 Marks
   aExplain the Laplace transform and region of convergence in detail.
   How to answer

   • Define Laplace transform bilateral/unilateral formula.
   • Define ROC and its significance.
   • Explain properties of ROC for causal, anti-causal, two-sided signals.
   • Give examples with pole-zero plot and ROC.
8. 7 Marks
   bDerive the Laplace and Fourier transform of following.

   1. i)$e^{-at}u(t)$
   2. ii)$t \cdot u(t)$
   How to answer

   • Write Laplace integral $X(s)=\int_{-\infty}^{\infty}x(t)e^{-st}dt$ and Fourier integral.
   • Derive for $e^{-at}u(t)$ to get $1/(s+a)$ and $1/(a+j\omega)$.
   • Derive for $t\cdot u(t)$ to get $1/s^2$ and related Fourier form.
   • Mention ROC and existence conditions.
9. 7 Marks
   aDescribe the block diagram representation of LTI continuous time system with its advantages.
   How to answer

   • Draw block diagram of LTI continuous-time system with input, system, output.
   • Explain components: adder, multiplier, integrator/delay.
   • Explain representation using differential equations / convolution.
   • List advantages e.g. analysis simplicity, modularity.
10. 7 Marks
    bExplain analog filters in brief. Also describe the properties of LTI system.
    How to answer

    • Define analog filter and its types.
    • Briefly explain low-pass, high-pass, band-pass with response.
    • State LTI properties: linearity, time-invariance, causality, stability.
    • Explain convolution, superposition implications.
11. 7 Marks
    aExplain the sampling of continuous time signals and aliasing.
    How to answer

    • Define sampling of continuous-time signal with sampling theorem.
    • Explain Nyquist rate and reconstruction.
    • Define aliasing and its cause $f_s < 2f_m$.
    • Explain prevention using anti-aliasing filter with diagram.
12. 7 Marks
    bDescribe the z-transform along with properties and suitable example.
    How to answer

    • Define z-transform formula $X(z)=\sum x[n]z^{-n}$ and ROC.
    • List properties: linearity, shifting, scaling, convolution.
    • Give suitable example e.g. unit step or exponential sequence.
    • Mention relation to DTFT.
13. 7 Marks
    aDescribe the state variable representation and matrix representation of system.
    How to answer

    • Define state variables, state vector.
    • Write state equations $\dot{X}=AX+BU$, $Y=CX+DU$.
    • Explain matrix representation A,B,C,D significance.
    • Give example of obtaining state model.
14. 7 Marks
    bIn LTI system, the input, output are related as $y(t) = \int_{-\infty}^{t} e^{-2(t-z)}x(z-3)dz$. Find impulse response of the system.
    How to answer

    • Identify given relation as convolution $y(t)=x(t)*h(t)$ with delay.
    • Substitute $x(t)=\delta(t)$ to find $h(t)$.
    • Simplify integral $y(t)=\int_{-\infty}^{t}e^{-2(t-z)}x(z-3)dz$.
    • Obtain impulse response expression with unit step and delay.
15. 14 Marks
    Write short notes on:

    1. i)Wavelet transform
    2. ii)DTFT and its properties
    3. iii)Digital filters
    4. iv)Inverse z-transform
    How to answer

    • Define wavelet transform, DTFT, digital filters, inverse z-transform.
    • Give formula / block diagram for each.
    • List key properties and applications.
    • Give example for each topic.