Package org.apache.commons.math4.transform

Class FastCosineTransform

java.lang.Object

org.apache.commons.math4.transform.FastCosineTransform

All Implemented Interfaces:

Function<double[],double[]>, UnaryOperator<double[]>, RealTransform

public class FastCosineTransform
extends Object
implements RealTransform

Implements the Fast Cosine Transform for transformation of one-dimensional real data sets. For reference, see James S. Walker, Fast Fourier Transforms, chapter 3 (ISBN 0849371635).

There are several variants of the discrete cosine transform. The present implementation corresponds to DCT-I, with various normalization conventions, which are specified by the parameter FastCosineTransform.Norm.

DCT-I is equivalent to DFT of an even extension of the data series. More precisely, if x₀, …, x_N-1 is the data set to be cosine transformed, the extended data set x₀^#, …, x_2N-3^# is defined as follows

• x_k^# = x_k if 0 ≤ k < N,
• x_k^# = x_2N-2-k if N ≤ k < 2N - 2.

Then, the standard DCT-I y₀, …, y_N-1 of the real data set x₀, …, x_N-1 is equal to half of the N first elements of the DFT of the extended data set x₀^#, …, x_2N-3^#
y_n = (1 / 2) ∑_k=0^2N-3 x_k^# exp[-2πi nk / (2N - 2)] k = 0, …, N-1.

The present implementation of the discrete cosine transform as a fast cosine transform requires the length of the data set to be a power of two plus one (N = 2ⁿ + 1). Besides, it implicitly assumes that the sampled function is even.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	FastCosineTransform.Norm	Normalization types.

Constructor Summary

Constructors

Constructor	Description
FastCosineTransform(FastCosineTransform.Norm normalization)
FastCosineTransform(FastCosineTransform.Norm normalization, boolean inverse)

Method Summary

Modifier and Type	Method	Description
double[]	apply(double[] f)	Returns the transform of the specified data set.
double[]	apply(DoubleUnaryOperator f, double min, double max, int n)	Returns the transform of the specified function.

Methods inherited from class java.lang.Object

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

Methods inherited from interface java.util.function.Function

andThen, compose

Constructor Detail

FastCosineTransform

public FastCosineTransform(FastCosineTransform.Norm normalization,
                           boolean inverse)

Parameters:

normalization - Normalization to be applied to the transformed data.

inverse - Whether to perform the inverse transform.

FastCosineTransform

public FastCosineTransform(FastCosineTransform.Norm normalization)

Parameters:

normalization - Normalization to be applied to the transformed data.

Method Detail

apply

public double[] apply(double[] f)

Returns the transform of the specified data set.

Specified by:

apply in interface Function<double[],double[]>

Specified by:

apply in interface RealTransform

Parameters:

f - the data array to be transformed (signal).

Returns:

the transformed array (spectrum).

Throws:

IllegalArgumentException - if the length of the data array is not a power of two plus one.

apply

public double[] apply(DoubleUnaryOperator f,
                      double min,
                      double max,
                      int n)

Returns the transform of the specified function.

Specified by:

apply in interface RealTransform

Parameters:

f - Function to be sampled and transformed.

min - Lower bound (inclusive) of the interval.

max - Upper bound (exclusive) of the interval.

n - Number of sample points.

Returns:

the result.

Throws:

IllegalArgumentException - if the number of sample points is not a power of two plus one, if the lower bound is greater than or equal to the upper bound, if the number of sample points is negative.