Apache Commons Math 3.6.1 · org.apache.commons.math3.transform.DctNormalization

public final Enum DctNormalization

Class Inheritance

java.lang.Object
java.lang.Enum
org.apache.commons.math3.transform.DctNormalization

This enumeration defines the various types of normalizations that can be applied to discrete cosine transforms (DCT). The exact definition of these normalizations is detailed below.

Field Summary

Modifier and Type	Field and Description
public static final DctNormalization	ORTHOGONAL_DCT_I Should be passed to the constructor of `FastCosineTransformer` to use the orthogonal normalization convention.
public static final DctNormalization	STANDARD_DCT_I Should be passed to the constructor of `FastCosineTransformer` to use the standard normalization convention.

Constructor Summary

Access	Constructor and Description
private	DctNormalization()

Modifier and Type	Method and Description
public static DctNormalization	valueOf(String name)
public static DctNormalization[]	values()

Modifier and Type

Method and Description

public static DctNormalization

valueOf(String name)

public static DctNormalization[]

values()

Field Detail

ORTHOGONAL_DCT_I back to summary

ORTHOGONAL_DCT_I	back to summary
public static final DctNormalization ORTHOGONAL_DCT_I Should be passed to the constructor of `FastCosineTransformer` to use the orthogonal normalization convention. The orthogonal DCT-I normalization convention is defined as follows forward transform: y_n = [2(N - 1)]^-1/2 [x₀ + (-1)ⁿx_N-1] + [2 / (N - 1)]^1/2 ∑_k=1^N-2 x_k cos[π nk / (N - 1)], inverse transform: x_k = [2(N - 1)]^-1/2 [y₀ + (-1)^ky_N-1] + [2 / (N - 1)]^1/2 ∑_n=1^N-2 y_n cos[π nk / (N - 1)], which makes the transform orthogonal. N is the size of the data sample.

public static final DctNormalization ORTHOGONAL_DCT_I

Should be passed to the constructor of FastCosineTransformer to use the orthogonal normalization convention. The orthogonal DCT-I normalization convention is defined as follows

forward transform: y_n = [2(N - 1)]^-1/2 [x₀ + (-1)ⁿx_N-1] + [2 / (N - 1)]^1/2 ∑_k=1^N-2 x_k cos[π nk / (N - 1)],
inverse transform: x_k = [2(N - 1)]^-1/2 [y₀ + (-1)^ky_N-1] + [2 / (N - 1)]^1/2 ∑_n=1^N-2 y_n cos[π nk / (N - 1)],

which makes the transform orthogonal. N is the size of the data sample.

STANDARD_DCT_I back to summary

STANDARD_DCT_I	back to summary
public static final DctNormalization STANDARD_DCT_I Should be passed to the constructor of `FastCosineTransformer` to use the standard normalization convention. The standard DCT-I normalization convention is defined as follows forward transform: y_n = (1/2) [x₀ + (-1)ⁿx_N-1] + ∑_k=1^N-2 x_k cos[π nk / (N - 1)], inverse transform: x_k = [1 / (N - 1)] [y₀ + (-1)^ky_N-1] + [2 / (N - 1)] ∑_n=1^N-2 y_n cos[π nk / (N - 1)], where N is the size of the data sample.

public static final DctNormalization STANDARD_DCT_I

Should be passed to the constructor of FastCosineTransformer to use the standard normalization convention. The standard DCT-I normalization convention is defined as follows

forward transform: y_n = (1/2) [x₀ + (-1)ⁿx_N-1] + ∑_k=1^N-2 x_k cos[π nk / (N - 1)],
inverse transform: x_k = [1 / (N - 1)] [y₀ + (-1)^ky_N-1] + [2 / (N - 1)] ∑_n=1^N-2 y_n cos[π nk / (N - 1)],

where N is the size of the data sample.

Constructor Detail

DctNormalization	back to summary
private DctNormalization()

valueOf	back to summary
public static DctNormalization valueOf(String name)

valueOf

back to summary

public static DctNormalization valueOf(String name)

values	back to summary
public static DctNormalization[] values()

values

back to summary

public static DctNormalization[] values()

public final Enum DctNormalization

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail