org.apache.commons.math3.transform
Class FastFourierTransformer

java.lang.Object
  org.apache.commons.math3.transform.FastFourierTransformer

All Implemented Interfaces:

Serializable

public class FastFourierTransformer
extends Object
implements Serializable

Implements the Fast Fourier Transform for transformation of one-dimensional real or complex data sets. For reference, see Applied Numerical Linear Algebra, ISBN 0898713897, chapter 6.

There are several variants of the discrete Fourier transform, with various normalization conventions, which are specified by the parameter DftNormalization.

The current implementation of the discrete Fourier transform as a fast Fourier transform requires the length of the data set to be a power of 2. This greatly simplifies and speeds up the code. Users can pad the data with zeros to meet this requirement. There are other flavors of FFT, for reference, see S. Winograd, On computing the discrete Fourier transform, Mathematics of Computation, 32 (1978), 175 - 199.

Since:

1.2

Version:

$Id: FastFourierTransformer.java 1385310 2012-09-16 16:32:10Z tn $

See Also:

DftNormalization, Serialized Form

Constructor Summary

FastFourierTransformer(DftNormalization normalization)
Creates a new instance of this class, with various normalization conventions.

Method Summary

Object	mdfft(Object mdca, TransformType type) Deprecated. see MATH-736
Complex[]	transform(Complex[] f, TransformType type) Returns the (forward, inverse) transform of the specified complex data set.
Complex[]	transform(double[] f, TransformType type) Returns the (forward, inverse) transform of the specified real data set.
Complex[]	transform(UnivariateFunction f, double min, double max, int n, TransformType type) Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
static void	transformInPlace(double[][] dataRI, DftNormalization normalization, TransformType type) Computes the standard transform of the specified complex data.

Methods inherited from class java.lang.Object

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

Constructor Detail

FastFourierTransformer

public FastFourierTransformer(DftNormalization normalization)

Creates a new instance of this class, with various normalization conventions.

Parameters:

normalization - the type of normalization to be applied to the transformed data

Method Detail

transformInPlace

public static void transformInPlace(double[][] dataRI,
                                    DftNormalization normalization,
                                    TransformType type)

Computes the standard transform of the specified complex data. The computation is done in place. The input data is laid out as follows

• dataRI[0][i] is the real part of the i-th data point,
• dataRI[1][i] is the imaginary part of the i-th data point.

Parameters:

dataRI - the two dimensional array of real and imaginary parts of the data

normalization - the normalization to be applied to the transformed data

type - the type of transform (forward, inverse) to be performed

Throws:

DimensionMismatchException - if the number of rows of the specified array is not two, or the array is not rectangular

MathIllegalArgumentException - if the number of data points is not a power of two

transform

public Complex[] transform(double[] f,
                           TransformType type)

Returns the (forward, inverse) transform of the specified real data set.

Parameters:

f - the real data array to be transformed

type - the type of transform (forward, inverse) to be performed

Returns:

the complex transformed array

Throws:

MathIllegalArgumentException - if the length of the data array is not a power of two

transform

public Complex[] transform(UnivariateFunction f,
                           double min,
                           double max,
                           int n,
                           TransformType type)

Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.

Parameters:

f - the function to be sampled and transformed

min - the (inclusive) lower bound for the interval

max - the (exclusive) upper bound for the interval

n - the number of sample points

type - the type of transform (forward, inverse) to be performed

Returns:

the complex transformed array

Throws:

NumberIsTooLargeException - if the lower bound is greater than, or equal to the upper bound

NotStrictlyPositiveException - if the number of sample points n is negative

MathIllegalArgumentException - if the number of sample points n is not a power of two

transform

public Complex[] transform(Complex[] f,
                           TransformType type)

Returns the (forward, inverse) transform of the specified complex data set.

Parameters:

f - the complex data array to be transformed

type - the type of transform (forward, inverse) to be performed

Returns:

the complex transformed array

Throws:

MathIllegalArgumentException - if the length of the data array is not a power of two

mdfft

@Deprecated
public Object mdfft(Object mdca,
                               TransformType type)

Deprecated. see MATH-736

Performs a multi-dimensional Fourier transform on a given array. Use transform(Complex[], TransformType) in a row-column implementation in any number of dimensions with O(N×log(N)) complexity with N = n₁ × n₂ ×n₃ × ... × n_d, where n_k is the number of elements in dimension k, and d is the total number of dimensions.

Parameters:

mdca - Multi-Dimensional Complex Array, i.e. Complex[][][][]

type - the type of transform (forward, inverse) to be performed

Returns:

transform of mdca as a Multi-Dimensional Complex Array, i.e. Complex[][][][]

Throws:

IllegalArgumentException - if any dimension is not a power of two