Contents NTRODUCTION PRELIMINARIES AND NOTATION I CHAPTER I: The What, Why, and How of Wavelets C. 1.- CHAPTER 2: The Continuous Wavelet Transform CHAPTER 3: Discrete Wavelet Transforms: frames 107 CHAPTER 4: Time-Frequency Density and Orthonormal Bases

single-gene disorder or monogenic disorder Some disorders result when a mutation causes the product of a single gene to be altered or missing. These disorders are inherited in simple patterns similar to or identical with those described by Mendel for certain discrete characteristics in garden peas. Therefore it's also called mendelian diseases

Have considered the vibrational behavior of a discrete system. How does one use this for a continuous structure? First need the concept of..... Influence Coefficients

What is Object-Oriented? Object orientation is an approach to software development that organizes both the problem ane nd its solution as a collection of discrete objects

Can be continuous Trajectory of a space shuttle Mass density in a cross-section of a brain · Can be discrete dNa base sequence Digital image pixels Can be 1-D,2-D,·N-D For this course: Focus on a single(1-D) independent variable which we call“time

Introduction Basic signal properties(dc, rms, dBm, and power) Fourier transform and spectra Linear systems and linear distortion Bandlimited signal and sampling Discrete Fourier transform Bandwidth of signal

Sampling Given a continuous time waveform, can we represent it using discrete samples? How often should we sample? Can we reproduce the original waveform?

Information content of a random variable Random variable x Outcome of a random experiment Discrete R V takes on values from a finite set of possible outcomes PMF: P(X=y)=Py) How much information is contained in the event X=y? Will the sun rise today Revealing the outcome of this experiment provides no information Will the Celtics win the NBa championship? Since this is unlikely, revealing yes provides more information than revealing Events that are less likely contain more information than likely events

Introduction Ideally, the system parameters along with the signal variables have infinite precision taking any value between -oo and · In practice, they can take only discrete values within a specified range since the registers of the digital machine where they are stored are of finite length

6.1 Introduction The convolution sum description of an LTI discrete-time system can, in principle, be used to implement the system For an IR finite-dimensional system this approach is not practical as here the impulse response is of infinite length · However, direct implementation of the IIR finite-dimensional system is practica