syllabus for a Signals and Systems course:

syllabus for a Signals and Systems course:

Unit I: Introduction to Signals and Systems

  • Classification of Signals: Continuous-time and discrete-time signals, periodic and aperiodic signals, even and odd signals
  • Basic Operations on Signals: Scaling, shifting, inversion, and addition
  • Classification of Systems: Linear and nonlinear, time-invariant and time-variant, causal and non-causal, stable and unstable systems

Unit II: Time-Domain Analysis of Continuous-Time Systems

  • Impulse Response and Convolution: Convolution integral, properties of convolution
  • Differential Equations: Representation of LTI systems, solution of differential equations using Laplace transforms
  • System Stability: BIBO stability, Routh-Hurwitz criterion

Unit III: Frequency-Domain Analysis of Continuous-Time Signals

  • Fourier Series: Representation of periodic signals, properties of Fourier series
  • Fourier Transform: Representation of aperiodic signals, properties of Fourier transform, applications
  • Laplace Transform: Region of convergence, inverse Laplace transform, applications to system analysis

Unit IV: Time-Domain Analysis of Discrete-Time Systems

  • Impulse Response and Convolution: Convolution sum, properties of convolution
  • Difference Equations: Representation of LTI systems, solution of difference equations using Z-transforms
  • System Stability: BIBO stability, Jury’s criterion

Unit V: Frequency-Domain Analysis of Discrete-Time Signals

  • Discrete-Time Fourier Transform (DTFT): Properties and applications
  • Discrete Fourier Transform (DFT): Properties, computation using FFT algorithms
  • Z-Transform: Region of convergence, inverse Z-transform, applications to system analysis

Unit VI: Sampling and Reconstruction

  • Sampling Theorem: Nyquist rate, aliasing, sampling of continuous-time signals
  • Reconstruction: Ideal reconstruction, practical reconstruction using zero-order hold and first-order hold

Unit VII: State-Space Analysis

  • State-Space Representation: State variables, state-space models for continuous and discrete systems
  • Solution of State Equations: State transition matrix, stability analysis using eigenvalues

Unit VIII: Applications of Signals and Systems

  • Communication Systems: Modulation and demodulation, signal transmission and reception
  • Control Systems: Feedback systems, stability analysis, PID controllers
  • Signal Processing: Filtering, signal enhancement, noise reduction

Practical/Lab Work

  • MATLAB Simulations: Signal generation, system analysis, Fourier and Laplace transforms
  • Experiments: Verification of theoretical concepts through practical experiments

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