G-NET II

Summary: This modules derives the Discrete-Time Fourier Series (DTFS), which is a fourier series type expansion for discrete-time, periodic functions. The module also takes some time to review complex sinusoids which will be used as our basis. Derivation of DTFS Complex Fourier Series and Their Properties Summary: This module shows how to find a signal's complex Fourier spectrum. It also lists several properties for that spectrum, including that it obeys Parseval's theorem. Fourier Series in a Nutshell Summary: This module will give a brief over of the key concepts involving the Fourier series and the tools used to decompose and approximate a given signal. Fourier Series: Eigenfunction Approach Summary: This module will introduce the Fourier Series and its Fourier coefficients using the concepts of eigenfunctions and basis. We will show several examples of how to decompose a signal and find the Fourier coefficients. Introducing the Fourier Series to LTI Systems Fourier Series Example Summary: This module provides an example of the Fourier Series representation of a half-wave rectified sinusoid. The Inverse Laplace Transform: Complex Integration The Inverse Laplace Transform Laplace Properties and Transforms Sampling Summary: This module deals with translating continuous time problem into discrete time Examing Reconstruction Relations Perfect Reconstruction FIR Filter Banks FIR Perfect-Reconstruction Conditions Summary: This module will drop the restrictive QMF conditions and focus on using FIR filters to achieve perfect reconstruction from filterbanks. Two-Branch Quadvalue Mirror Filterbank (QMF) Summary: This module covers Quadrature Mirror Filterbanks (QMF) and looks at the new design choices they implement and how they are used in perfect reconstruction. Quadrature Mirror Filterbanks Digital Signal Processing (Ohio State EE700)