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java.lang.Objectorg.apache.commons.math3.transform.FastCosineTransformer
public class FastCosineTransformer
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
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.
| Constructor Summary | |
|---|---|
FastCosineTransformer(DctNormalization normalization)
Creates a new instance of this class, with various normalization conventions. |
|
| Method Summary | |
|---|---|
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 |
|---|
public FastCosineTransformer(DctNormalization normalization)
normalization - the type of normalization to be applied to the
transformed data| Method Detail |
|---|
public double[] transform(double[] f,
TransformType type)
throws MathIllegalArgumentException
transform in interface RealTransformerf - the real data array to be transformed (signal)type - the type of transform (forward, inverse) to be performed
MathIllegalArgumentException - if the length of the data array is
not a power of two plus one
public double[] transform(UnivariateFunction f,
double min,
double max,
int n,
TransformType type)
throws MathIllegalArgumentException
transform in interface RealTransformerf - the function to be sampled and transformedmin - the (inclusive) lower bound for the intervalmax - the (exclusive) upper bound for the intervaln - the number of sample pointstype - the type of transform (forward, inverse) to be performed
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
protected double[] fct(double[] f)
throws MathIllegalArgumentException
f - the real data array to be transformed
MathIllegalArgumentException - if the length of the data array is
not a power of two plus one
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