Signals and Systems

Unit-wise syllabus

• Introduction
  Definition and classification of signals and systems; Operations on signals: time-shifting, time-scaling, amplitude-shifting/scaling; Complex exponential and sinusoidal signals; singularity functions (impulse, step, signum, ramp); Analogy between vectors and signals; orthogonal signal space; mean square error; orthogonality in complex functions
• Fourier Series and Fourier Transform
  Fourier series of continuous-time periodic signals; Dirichlet's conditions; Trigonometric and exponential Fourier series; complex Fourier spectrum; Fourier transform of standard and periodic signals; properties; Introduction to Hilbert transform
• Analysis of Linear Systems
  Linear system, impulse response, LTI and LTV systems; Convolution in time and frequency domain; transfer function of an LTI system; Filter characteristics; distortionless transmission; signal and system bandwidth; Ideal LPF/HPF/BPF; Paley-Wiener criterion; bandwidth-rise time relation
• Laplace Transforms
  Region of convergence (ROC) and constraints for various signal classes; Properties of Laplace transforms; inverse Laplace transform; Relation between Laplace transform and Fourier transform; Laplace transform via waveform synthesis
• Sampling Theorem and Z-Transforms
  Sampling theorem for band-limited signals; impulse, natural and flat-top sampling; Reconstruction; aliasing; band-pass sampling; Z-transform of a discrete sequence; ROC; inverse Z-transform; properties; Distinction between Laplace, Fourier and Z transforms

Download