Signals as Vectors

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Signals as Vectors

It appears that you are using AdBlocking software. The cost of running this website is covered by advertisements. If you like it please feel free to a small amount of money to secure the future of this website.

<< Previous page  TOC  INDEX  Next page >>

Signals as Vectors

For the DFT, all signals and spectra are length $N$. A length $N$ sequence$x$ can be denoted by $x(n)$, $n=0,1,2,\, where $x(n)$ may be real ($x\) or complex ($x\). We now wish to regard $x$ as avector $\6.1 in an $N$ dimensional vector space. That is, each sample $x(n)$ is regarded as a coordinate in that space. A vector $\ is mathematically a single point in $N$-space represented by a list of coordinates $(x_0,x_1,x_2,\ called an $N$-tuple. (The notation $x_n$ means the same thing as $x(n)$.) It can be interpreted geometrically as an arrow in $N$-space from the origin $\ to the point $\.

We define the following as equivalent:

\

where $x_n \ is the $n$th sample of the signal (vector) $x$. From now on, unless specifically mentioned otherwise, all signals are length $N$.



Subsections

<< Previous page  TOC  INDEX  Next page >>

 

© 1998-2017 – Nicola Asuni - Tecnick.com - All rights reserved.
about - disclaimer - privacy