edu.princeton.cs.algs4

Class FFT

Object

edu.princeton.cs.algs4.FFT

public class FFT
extends Object

The FFT class provides methods for computing the FFT (Fast-Fourier Transform), inverse FFT, linear convolution, and circular convolution of a complex array.

It is a bare-bones implementation that runs in n log n time, where n is the length of the complex array. For simplicity, n must be a power of 2. Our goal is to optimize the clarity of the code, rather than performance. It is not the most memory efficient implementation because it uses objects to represent complex numbers and it re-allocates memory for the subarray, instead of doing in-place or reusing a single temporary array.

This computes correct results if all arithmetic performed is without floating-point rounding error or arithmetic overflow. In practice, there will be floating-point rounding error.

For additional documentation, see Section 9.9 of Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.

Author:

Robert Sedgewick, Kevin Wayne

Method Summary

Modifier and Type	Method and Description
static Complex[]	cconvolve(Complex[] x, Complex[] y) Returns the circular convolution of the two specified complex arrays.
static Complex[]	convolve(Complex[] x, Complex[] y) Returns the linear convolution of the two specified complex arrays.
static Complex[]	fft(Complex[] x) Returns the FFT of the specified complex array.
static Complex[]	ifft(Complex[] x) Returns the inverse FFT of the specified complex array.
static void	main(String[] args) Unit tests the FFT class.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

fft

public static Complex[] fft(Complex[] x)

Returns the FFT of the specified complex array.

Parameters:

x - the complex array

Returns:

the FFT of the complex array x

Throws:

IllegalArgumentException - if the length of x is not a power of 2

ifft

public static Complex[] ifft(Complex[] x)

Returns the inverse FFT of the specified complex array.

Parameters:

x - the complex array

Returns:

the inverse FFT of the complex array x

Throws:

IllegalArgumentException - if the length of x is not a power of 2

cconvolve

public static Complex[] cconvolve(Complex[] x,
                                  Complex[] y)

Returns the circular convolution of the two specified complex arrays.

Parameters:

x - one complex array

y - the other complex array

Returns:

the circular convolution of x and y

Throws:

IllegalArgumentException - if the length of x does not equal the length of y or if the length is not a power of 2

convolve

public static Complex[] convolve(Complex[] x,
                                 Complex[] y)

Returns the linear convolution of the two specified complex arrays.

Parameters:

x - one complex array

y - the other complex array

Returns:

the linear convolution of x and y

Throws:

IllegalArgumentException - if the length of x does not equal the length of y or if the length is not a power of 2

main

public static void main(String[] args)

Unit tests the FFT class.

Parameters:

args - the command-line arguments