IDFT Interface Reference

Discrete Fourier Transformation. More...

Inheritance diagram for IDFT:

List of all members.

Public Member Functions

Complex[] DFT (Complex[] a)

Discrete Fourier Transform.

Complex[] InverseDFT (Complex[] y)

Inverse Discrete Fourier Transform.

string ToString ()

Name of the DFT algorithm.

Detailed Description

Discrete Fourier Transformation.

This interface specifies two functions:

Discrete Fourier Transform, which takes a vector of cooeficients $\mathbf{a}=[a_0,\ldots,a_{n-1}]$ of a polynomial $A(x) = a_{n-1} * x^{n-1} + \ldots + a_1 * x + a_0$ and returns the vector of values $\mathbf{y}=[A(\omega_n^0),\ldots,A(\omega_n^{n-1})]$ , where $\omega_n$ is the primitive n-th root of unity, i.e. the complex number such that $argument(\omega_n)=\frac{2\pi}{n}$ and $modulus(\omega_n)=1$ .
Inverse Discrete Fourier Transform, which takes the vector of values $\mathbf{y}=[y_0,\ldots,y_{n-1}]$ and returns the vector of cooeficients $\mathbf{a}=[a_0,\ldots,a_{n-1}]$ of a polynomial $A(x) = a_{n-1} * x^{n-1} + \ldots + a_1 * x + a_0$ such that $y_i = A(\omega_n^i)$ for $i\in\{1,\ldots,n-1\}$ , where $\omega_n$ is the primitive n-th root of unity.

For ease of implementation the n can be assumed to be a power of 2.

Definition at line 26 of file IDFT.cs.

Complex [] DFT ( Complex[] a )

Discrete Fourier Transform.

Parameters:

a

table whos length is a power of 2.

Complex [] InverseDFT ( Complex[] y )

Inverse Discrete Fourier Transform.

Parameters:

y

table whos length is a power of 2.

string ToString ( )

Name of the DFT algorithm.

The documentation for this interface was generated from the following file:


Public Member Functions
Complex[]	DFT (Complex[] a)
	Discrete Fourier Transform.
Complex[]	InverseDFT (Complex[] y)
	Inverse Discrete Fourier Transform.
string	ToString ()
	Name of the DFT algorithm.