Counting Lattice Paths Using Fourier Methods by Shaun Ault & Charles Kicey

Author:Shaun Ault & Charles Kicey
Language: eng
Format: epub
ISBN: 9783030266967
Publisher: Springer International Publishing

(3.10)

where , , and the sum is understood to be over all such that in each component. Similarly, the inverse DFT of a function is a function of given by the formula:

(3.11)

It is straightforward to show that (in other words, as operators). There are no issues of convergence since the sums are finite.

Let’s explore how works on a function of particular importance. Consider the delta function, which we define on as follows:

The function has value zero at all points except the origin at which its value is 1. Using a shift operator, we can create a delta function whose only nonzero value occurs at .

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.