Signals and Systems

Signals and systems. Linear time-invariant systems. Fourier analysis for continuous-time signals and systems (Fourier series, Fourier transform) . Laplace transform. Fourier series representation of discrete-time periodic signals. The discrete-time Fourier transform. The z-transform. The discrete Fourier transform. Sampling. Programming in MATLAB algorithms for speech processing in cellular phones and audio coding in MP3 players.

Objectives

Cognitive: Thorough grasp of signals as information bearing carriers. Acquaintance with linear system theory; Unified and comparative treatment of continuous-time and discrete-time signals and systems; Introduce the frequency content of a signal as latent information inherent in its time-domain representation. Treatment of discrete-time signal transforms as algorithms of their continuous-time counterparts. Skills: Promoting analytic skills; Building the necessary theoretical foundation for the transition from system analysis to system design and proceeding to advanced studies in image processing, speech and audio processing, biomedical signal processing. Programming in MATLAB speech processing and audio coding applications.

Prerequisites

Prior exposition to linear algebra, calculus of functions of one independent real variable, complex analysis, and differential equations can facilitate the faster grasping of the concepts introduced.

Syllabus

• Unit 1: Introduction • Unit2: Mathematical representation of signals and systems • Unit 3: Linear time-invariant systems • Unit 4: Fourier analysis for continuous-time signals and systems – Periodic signals • Unit 5: Fourier analysis for continuous-time signals and systems- Fourier transform • Unit 6: Laplace transform • Unit 7: Fourier analysis for discrete-time signals and systems • Unit 8: Z transform • Unit 9: Sampling