EC-402 Signals and Systems - Jun 2026 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 a Signal. Classify signals as Continuous-Time and Discrete-Time with suitable examples.
   How to answer

   • Definition of signal as function of independent variable carrying information
   • Continuous-time signal definition with example e.g. x(t)
   • Discrete-time signal definition with example e.g. x[n]
   • Diagrammatic distinction and examples
2. 7 Marks
   bExplain the following classifications of signals:

   1. i)Periodic and Aperiodic
   2. ii)Deterministic and Random
   3. iii)Energy and Power
   4. iv)Even and Odd
   How to answer

   • Definition of periodic vs aperiodic with condition
   • Deterministic vs random signals
   • Energy vs power signals with formulas
   • Even vs odd signals with decomposition
3. 7 Marks
   aExplain the basic operations performed on Continuous-Time and Discrete-Time Signals.
   How to answer

   • Time shifting, reversal, scaling operations
   • Amplitude scaling, addition, multiplication
   • Differentiation, integration for CT; differencing, accumulation for DT
   • Examples with sketches
4. 7 Marks
   bDefine a System. Explain the classification of systems as:

   1. i)Linear and Nonlinear
   2. ii)Time-Invariant and Time-Variant
   3. iii)Causal and Non-Causal
   4. iv)Static and Dynamic
   How to answer

   • Definition of system
   • Linear vs nonlinear with superposition test
   • Time-invariant vs time-variant, causal vs non-causal
   • Static vs dynamic systems with examples
5. 7 Marks
   aExplain the Impulse Response of Discrete-Time LTI Systems. Derive the Convolution Sum.
   How to answer

   • Impulse response h[n] as response to delta[n]
   • Representation of arbitrary input as shifted impulses
   • Use of linearity and time-invariance
   • Derivation of y[n] = x[n] * h[n] convolution sum formula
6. 7 Marks
   bExplain the following realization structures:

   1. i)Direct Form-I
   2. ii)Direct Form-II
   3. iii)Cascade Form
   4. iv)Parallel Form
   How to answer

   • Block diagram of Direct Form-I
   • Block diagram of Direct Form-II with reduced delays
   • Cascade form using second-order sections
   • Parallel form using partial fractions
7. 7 Marks
   aDefine the Z-Transform. Explain the Region of Convergence (ROC) for finite and infinite sequences.
   How to answer

   • Definition of Z-transform X(z) summation formula
   • ROC concept and pole dependence
   • ROC for finite-duration sequences
   • ROC for infinite-duration causal/anticausal sequences
8. 7 Marks
   bExplain the important properties of the Z-Transform. Describe the methods for obtaining the Inverse Z-Transform.
   How to answer

   • Linearity, time-shifting, scaling properties
   • Convolution, differentiation, initial/final value theorems
   • Partial fraction inversion method
   • Power series and contour integration methods
9. 7 Marks
   aExplain the relationship between the Discrete-Time Fourier Transform (DTFT) and the Z-Transform.
   How to answer

   • DTFT as Z-transform on unit circle
   • Formula X(e^{jω}) = X(z)|_{z=e^{jω}}
   • ROC must include unit circle condition
   • Relation in analysis of LTI frequency response
10. 7 Marks
    bExplain the Unilateral Z-Transform. State its advantages in the analysis of causal systems.
    How to answer

    • Definition of unilateral Z-transform for n>=0
    • Difference from bilateral transform
    • Advantages for initial conditions and causal systems
    • Application to difference equations
11. 7 Marks
    aExplain the Discrete-Time Fourier Series (DTFS). Discuss its properties and applications.
    How to answer

    • Definition of DTFS for periodic sequences
    • Analysis and synthesis equations
    • Properties: linearity, shift, periodicity
    • Applications in spectral analysis
12. 7 Marks
    bExplain the Fourier Transform of Discrete-Time Aperiodic Signals. State its convergence conditions.
    How to answer

    • DTFT definition summation formula
    • Existence and absolute summability condition
    • Convergence conditions explanation
    • Examples of aperiodic signals
13. 7 Marks
    aExplain the Fourier Transform of Periodic Discrete-Time Signals. State its practical applications.
    How to answer

    • Fourier transform using impulses for periodic signals
    • Relation to DTFS coefficients
    • Spectrum as train of impulses
    • Practical applications in filtering and communication
14. 7 Marks
    bExplain the State-Space Representation of dynamic systems. Discuss Multi-Input Multi-Output (MIMO) systems.
    How to answer

    • State equations x_dot = Ax+Bu, y = Cx+Du
    • Concept of state vector and state-space
    • MIMO representation with matrices
    • Example of multi-input multi-output system
15. 7 Marks
    aDefine the State-Transition Matrix. Explain its importance in dynamic system analysis.
    How to answer

    • Definition phi(t) = e^{At}
    • Properties and computation methods
    • Role in zero-input and zero-state response
    • Importance in stability and controllability analysis
16. 7 Marks
    bState and explain the Sampling Theorem. Discuss the Reconstruction of Sampled Signals.
    How to answer

    • Nyquist sampling theorem statement fs >= 2fm
    • Aliasing and Nyquist rate explanation
    • Ideal low-pass reconstruction formula
    • Block diagram of sampling and reconstruction