org.apache.commons.math.transform

Class FastCosineTransformer

java.lang.Object

org.apache.commons.math.transform.FastCosineTransformer

All Implemented Interfaces:

RealTransformer

public class FastCosineTransformer
extends java.lang.Object
implements RealTransformer

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

FCT is its own inverse, up to a multiplier depending on conventions. The equations are listed in the comments of the corresponding methods.

Different from FFT and FST, FCT requires the length of data set to be power of 2 plus one. Users should especially pay attention to the function transformation on how this affects the sampling.

As of version 2.0 this no longer implements Serializable

Since:

1.2

Constructor Summary

Constructors

Constructor and Description
FastCosineTransformer() Construct a default transformer.

Method Summary

Modifier and Type	Method and Description
double[]	inversetransform(double[] f) Inversely transform the given real data set.
double[]	inversetransform(UnivariateRealFunction f, double min, double max, int n) Inversely transform the given real function, sampled on the given interval.
double[]	inversetransform2(double[] f) Inversely transform the given real data set.
double[]	inversetransform2(UnivariateRealFunction f, double min, double max, int n) Inversely transform the given real function, sampled on the given interval.
double[]	transform(double[] f) Transform the given real data set.
double[]	transform(UnivariateRealFunction f, double min, double max, int n) Transform the given real function, sampled on the given interval.
double[]	transform2(double[] f) Transform the given real data set.
double[]	transform2(UnivariateRealFunction f, double min, double max, int n) Transform the given real function, sampled on the given interval.

Methods inherited from class java.lang.Object

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

Constructor Detail

FastCosineTransformer

public FastCosineTransformer()

Construct a default transformer.

Method Detail

transform

public double[] transform(double[] f)
                   throws java.lang.IllegalArgumentException

Transform the given real data set.

The formula is F_n = (1/2) [f₀ + (-1)ⁿ f_N] + ∑_k=1^N-1 f_k cos(π nk/N)

Specified by:

transform in interface RealTransformer

Parameters:

f - the real data array to be transformed

Returns:

the real transformed array

Throws:

java.lang.IllegalArgumentException - if any parameters are invalid

transform

public double[] transform(UnivariateRealFunction f,
                          double min,
                          double max,
                          int n)
                   throws FunctionEvaluationException,
                          java.lang.IllegalArgumentException

Transform the given real function, sampled on the given interval.

The formula is F_n = (1/2) [f₀ + (-1)ⁿ f_N] + ∑_k=1^N-1 f_k cos(π nk/N)

Specified by:

transform in interface RealTransformer

Parameters:

f - the function to be sampled and transformed

min - the lower bound for the interval

max - the upper bound for the interval

n - the number of sample points

Returns:

the real transformed array

Throws:

FunctionEvaluationException - if function cannot be evaluated at some point

java.lang.IllegalArgumentException - if any parameters are invalid

transform2

public double[] transform2(double[] f)
                    throws java.lang.IllegalArgumentException

Transform the given real data set.

The formula is F_n = √(1/2N) [f₀ + (-1)ⁿ f_N] + √(2/N) ∑_k=1^N-1 f_k cos(π nk/N)

Parameters:

f - the real data array to be transformed

Returns:

the real transformed array

Throws:

java.lang.IllegalArgumentException - if any parameters are invalid

transform2

public double[] transform2(UnivariateRealFunction f,
                           double min,
                           double max,
                           int n)
                    throws FunctionEvaluationException,
                           java.lang.IllegalArgumentException

Transform the given real function, sampled on the given interval.

The formula is F_n = √(1/2N) [f₀ + (-1)ⁿ f_N] + √(2/N) ∑_k=1^N-1 f_k cos(π nk/N)

Parameters:

f - the function to be sampled and transformed

min - the lower bound for the interval

max - the upper bound for the interval

n - the number of sample points

Returns:

the real transformed array

Throws:

FunctionEvaluationException - if function cannot be evaluated at some point

java.lang.IllegalArgumentException - if any parameters are invalid

inversetransform

public double[] inversetransform(double[] f)
                          throws java.lang.IllegalArgumentException

Inversely transform the given real data set.

The formula is f_k = (1/N) [F₀ + (-1)^k F_N] + (2/N) ∑_n=1^N-1 F_n cos(π nk/N)

Specified by:

inversetransform in interface RealTransformer

Parameters:

f - the real data array to be inversely transformed

Returns:

the real inversely transformed array

Throws:

java.lang.IllegalArgumentException - if any parameters are invalid

inversetransform

public double[] inversetransform(UnivariateRealFunction f,
                                 double min,
                                 double max,
                                 int n)
                          throws FunctionEvaluationException,
                                 java.lang.IllegalArgumentException

Inversely transform the given real function, sampled on the given interval.

The formula is f_k = (1/N) [F₀ + (-1)^k F_N] + (2/N) ∑_n=1^N-1 F_n cos(π nk/N)

Specified by:

inversetransform in interface RealTransformer

Parameters:

f - the function to be sampled and inversely transformed

min - the lower bound for the interval

max - the upper bound for the interval

n - the number of sample points

Returns:

the real inversely transformed array

Throws:

FunctionEvaluationException - if function cannot be evaluated at some point

java.lang.IllegalArgumentException - if any parameters are invalid

inversetransform2

public double[] inversetransform2(double[] f)
                           throws java.lang.IllegalArgumentException

Inversely transform the given real data set.

The formula is f_k = √(1/2N) [F₀ + (-1)^k F_N] + √(2/N) ∑_n=1^N-1 F_n cos(π nk/N)

Parameters:

f - the real data array to be inversely transformed

Returns:

the real inversely transformed array

Throws:

java.lang.IllegalArgumentException - if any parameters are invalid

inversetransform2

public double[] inversetransform2(UnivariateRealFunction f,
                                  double min,
                                  double max,
                                  int n)
                           throws FunctionEvaluationException,
                                  java.lang.IllegalArgumentException

Inversely transform the given real function, sampled on the given interval.

The formula is f_k = √(1/2N) [F₀ + (-1)^k F_N] + √(2/N) ∑_n=1^N-1 F_n cos(π nk/N)

Parameters:

f - the function to be sampled and inversely transformed

min - the lower bound for the interval

max - the upper bound for the interval

n - the number of sample points

Returns:

the real inversely transformed array

Throws:

FunctionEvaluationException - if function cannot be evaluated at some point

java.lang.IllegalArgumentException - if any parameters are invalid