January 2008
Intermediate to advanced
572 pages
12h 49m
English
book
Discrete Wavelet Transformations: An Elementary Approach with Applications
by Patrick J. Van Fleet
Content preview from Discrete Wavelet Transformations: An Elementary Approach with Applications
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
CHAPTER 4
COMPLEX NUMBERS AND FOURIER SERIES
Complex numbers and Fourier series play vital roles in digital and signal processing. In this chapter we introduce the complex plane and complex numbers and discuss arithmetic with complex numbers. In Section 4.2 we introduce the complex exponential via Euler’s famous formula.
As you progress through the book, you will learn why Fourier series are so important. The idea is similar to that of MacLaurin series — we rewrite the given function in terms of basic elements. While the family of functions xn, n = 0, 1, … serve as building blocks for MacLaurin series, the complex exponentials eikω, k 
are used to construct Fourier series. Fourier series coefficients hold much information about the transformations we develop in this book. As you will see in Chapters 8 and 10, once we arrive at a set of desirable conditions for constructing our transformations, it is natural to reformulate the conditions in terms of Fourier series! Thus, a mastery of the material in Section 4.3 is essential for understanding transformation construction that follows later in the text.
4.1 THE COMPLEX PLANE AND ARITHMETIC
In this section we review complex numbers and some of their basic properties. We will also discuss elementary complex arithmetic, modulus, and conjugates. ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.