FastCosineTransformer (Apache Commons Math 3.5 API)

java.lang.Object
- org.apache.commons.math3.transform.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, …, 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.
Since:

1.2

See Also:
Serialized Form

Constructor Summary

Constructors
Constructor and Description

FastCosineTransformer(DctNormalization normalization)
Creates a new instance of this class, with various normalization conventions.

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

Class FastCosineTransformer

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

FastCosineTransformer

Method Detail

transform

transform

fct