public class FastCosineTransformer extends Object implements RealTransformer, Serializable
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 and Description |
|---|
FastCosineTransformer(DctNormalization normalization)
Creates a new instance of this class, with various normalization
conventions.
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| 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.
|
public FastCosineTransformer(DctNormalization normalization)
normalization - the type of normalization to be applied to the
transformed datapublic 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 performedMathIllegalArgumentException - if the length of the data array is
not a power of two plus onepublic 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 performedNonMonotonicSequenceException - if the lower bound is greater than, or equal to the upper boundNotStrictlyPositiveException - if the number of sample points is negativeMathIllegalArgumentException - if the number of sample points is
not a power of two plus oneprotected double[] fct(double[] f)
throws MathIllegalArgumentException
f - the real data array to be transformedMathIllegalArgumentException - if the length of the data array is
not a power of two plus oneCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.