org.apache.commons.math3.transform

## Class FastCosineTransformer

• All Implemented Interfaces:
Serializable, RealTransformer

public class FastCosineTransformer
extends Object
implements RealTransformer, Serializable
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 DctNormalization.

DCT-I is equivalent to DFT of an even extension of the data series. More precisely, if x0, …, xN-1 is the data set to be cosine transformed, the extended data set x0#, …, x2N-3# is defined as follows

• xk# = xk if 0 ≤ k < N,
• xk# = x2N-2-k if N ≤ k < 2N - 2.

Then, the standard DCT-I y0, …, yN-1 of the real data set x0, …, xN-1 is equal to half of the N first elements of the DFT of the extended data set x0#, …, x2N-3#
yn = (1 / 2) ∑k=02N-3 xk# 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.

Since:
1.2
Serialized Form
• ### Constructor Summary

Constructors
Constructor and Description
FastCosineTransformer(DctNormalization normalization)
Creates a new instance of this class, with various normalization conventions.
• ### Method Summary

Methods
Modifier and Type Method and Description
protected double[] fct(double[] f)
Perform the FCT algorithm (including inverse).
double[] transform(double[] f, TransformType type)
Returns the (forward, inverse) transform of the specified real data set.
double[] 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.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### FastCosineTransformer

public FastCosineTransformer(DctNormalization 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

• #### transform

public double[] transform(double[] f,
TransformType type)
throws MathIllegalArgumentException
Returns the (forward, inverse) transform of the specified real data set.
Specified by:
transform in interface RealTransformer
Parameters:
f - the real data array to be transformed (signal)
type - the type of transform (forward, inverse) to be performed
Returns:
the real transformed array (spectrum)
Throws:
MathIllegalArgumentException - if the length of the data array is not a power of two plus one
• #### transform

public double[] transform(UnivariateFunction f,
double min,
double max,
int n,
TransformType type)
throws MathIllegalArgumentException
Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
Specified by:
transform in interface RealTransformer
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 real transformed array
Throws:
NonMonotonicSequenceException - if the lower bound is greater than, or equal to the upper bound
NotStrictlyPositiveException - if the number of sample points is negative
MathIllegalArgumentException - if the number of sample points is not a power of two plus one
• #### fct

protected double[] fct(double[] f)
throws MathIllegalArgumentException
Perform the FCT algorithm (including inverse).
Parameters:
f - the real data array to be transformed
Returns:
the real transformed array
Throws:
MathIllegalArgumentException - if the length of the data array is not a power of two plus one