Signals and Systems

Definition and classification of signals and systems; Operations on signals: time-shifting, time-scaling, amplitude-shifting and amplitude-scaling; Complex exponential and sinusoidal signals; Singularity functions: impulse, step, signum and ramp functions

Fourier series of continuous-time periodic signals; Dirichlet's conditions; Trigonometric and exponential Fourier series; relation between them; complex Fourier spectrum; Deriving the Fourier transform from the Fourier series; Fourier transform of standard signals; Properties of Fourier transforms; transforms involving impulse and signum functions

Auto-correlation and cross-correlation of functions and their properties; Energy density spectrum, Parseval's theorem, power density spectrum; relation between convolution and correlation; Sampling theorem for band-limited signals; impulse, natural and flat-top sampling; Reconstruction of a signal from its samples; aliasing

Concept of region of convergence (ROC) for Laplace transforms and constraints for various signal classes; Properties of Laplace transforms; Inverse Laplace transform; relation between Laplace transform and Fourier transform; Laplace transform of signals using waveform synthesis

Concept of the Z-transform of a discrete sequence; Region of convergence in the Z-transform and constraints for various signal classes; Inverse Z-transform and properties of Z-transforms; Distinction between Laplace, Fourier and Z transforms