Module ojalgo

Package org.ojalgo.data.transform

Class DiscreteFourierTransform

java.lang.Object

org.ojalgo.data.transform.DiscreteFourierTransform

All Implemented Interfaces:

DataTransform<Access1D<?>,MatrixStore<ComplexNumber>>

public abstract class DiscreteFourierTransform
extends Object
implements DataTransform<Access1D<?>,MatrixStore<ComplexNumber>>

The discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. The DFT is therefore said to be a frequency domain representation of the original input sequence.

The fast Fourier transform (FFT) is an algorithm for computing the DFT; it achieves its high speed by storing and reusing results of computations as it progresses.

Calling the factory method newInstance(int) will return an FFT implementation if the size is a power of 2, and a full matrix implementation otherwise.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	DiscreteFourierTransform.Directive

Method Summary

Modifier and Type	Method	Description
static int[]	getBitReversedIndices(int size)
static Access1D<ComplexNumber>	getUnitRoots(int size)
final void	inverse(Access1D<?> input, Mutate2D.ModifiableReceiver<ComplexNumber> output)
final MatrixStore<ComplexNumber>	inverse(Access1D<ComplexNumber> input)
static MatrixStore<ComplexNumber>	inverse2D(MatrixStore<?> input)
static DiscreteFourierTransform	newInstance(int size)	Will return a functioning instance for any size, but if you want fast transformation (FFT) it needs to be a power of 2.
static <M extends Mutate2D> M	newVandermonde(Factory2D<M> factory, int size)
static MatrixC128	newVandermondeMatrix(int size)
static MatrixStore<ComplexNumber>	sample(DoubleUnaryOperator function, PrimitiveFunction.SampleDomain sampleDomain)	Sample, and transform, a function using the Discrete Fourier Transform.
static MatrixStore<ComplexNumber>	sample(PeriodicFunction function, int nbSamples)
static <N extends Comparable<N>> MatrixStore<N>	shift(MatrixStore<N> matrix)	There is a symmetry in the DFT matrix.
MatrixStore<ComplexNumber>	transform(double... input)
final MatrixStore<ComplexNumber>	transform(Access1D<?> input)
abstract void	transform(Access1D<?> input, DiscreteFourierTransform.Directive directive, Mutate2D.ModifiableReceiver<ComplexNumber> output)
final void	transform(Access1D<?> input, Mutate2D.ModifiableReceiver<ComplexNumber> output)
static MatrixStore<ComplexNumber>	transform2D(MatrixStore<?> input)	Perform a 2D Discrete Fourier Transform on the input matrix.
static void	transform2D(MatrixStore<?> input, DiscreteFourierTransform.Directive directive, TransformableRegion<ComplexNumber> output)

Methods inherited from class java.lang.Object

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

Method Details

getBitReversedIndices

public static int[] getBitReversedIndices(int size)

getUnitRoots

public static Access1D<ComplexNumber> getUnitRoots(int size)

inverse2D

public static MatrixStore<ComplexNumber> inverse2D(MatrixStore<?> input)

newInstance

public static DiscreteFourierTransform newInstance(int size)

Will return a functioning instance for any size, but if you want fast transformation (FFT) it needs to be a power of 2.

newVandermonde

public static <M extends Mutate2D> M newVandermonde(Factory2D<M> factory,
 int size)

newVandermondeMatrix

public static MatrixC128 newVandermondeMatrix(int size)

sample

public static MatrixStore<ComplexNumber> sample(DoubleUnaryOperator function,
 PrimitiveFunction.SampleDomain sampleDomain)

Sample, and transform, a function using the Discrete Fourier Transform.

sample

public static MatrixStore<ComplexNumber> sample(PeriodicFunction function,
 int nbSamples)

See Also:

• sample(DoubleUnaryOperator, PrimitiveFunction.SampleDomain)

shift

public static <N extends Comparable<N>>
MatrixStore<N> shift(MatrixStore<N> matrix)

There is a symmetry in the DFT matrix. The first half of the rows (and columns) are the complex conjugates of the second half. Furthermore, the first half correspond to positive frequencies, and the second half to negative frequencies.

Re-arranging the elements of a matrix, shifting the first and second halves of the rows (and columns), puts the zero-frequency term in the middle, and the conjugate pairs at equal distances from the centre.

This is useful when displaying the 2D DFT matrix as an image.

To revert the shift, simply call shift(MatrixStore) again. However, this will not work correctly if there's an odd number of rows or columns. In that case the second call will not correctly revert the position of the zero-frequency term – it will end up in the last row/column instead of in the first.

transform2D

public static MatrixStore<ComplexNumber> transform2D(MatrixStore<?> input)

Perform a 2D Discrete Fourier Transform on the input matrix. The output will be a complex matrix of the same size.

transform2D

public static void transform2D(MatrixStore<?> input,
 DiscreteFourierTransform.Directive directive,
 TransformableRegion<ComplexNumber> output)

inverse

public final void inverse(Access1D<?> input,
 Mutate2D.ModifiableReceiver<ComplexNumber> output)

inverse

public final MatrixStore<ComplexNumber> inverse(Access1D<ComplexNumber> input)

transform

public final MatrixStore<ComplexNumber> transform(Access1D<?> input)

Specified by:

transform in interface DataTransform<Access1D<?>,MatrixStore<ComplexNumber>>

transform

public abstract void transform(Access1D<?> input,
 DiscreteFourierTransform.Directive directive,
 Mutate2D.ModifiableReceiver<ComplexNumber> output)

transform

public final void transform(Access1D<?> input,
 Mutate2D.ModifiableReceiver<ComplexNumber> output)

transform

public MatrixStore<ComplexNumber> transform(double... input)