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 |
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FastCosineTransformer(DctNormalization normalizationIn)
Creates a new instance of this class, with various normalization
conventions.
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Modifier and Type | Method and Description |
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protected double[] |
fct(double[] f)
Perform the FCT algorithm (including inverse).
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double[] |
transform(double[] f,
TransformType type)
Returns the (forward, inverse) transform of the specified real data set.
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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.
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public FastCosineTransformer(DctNormalization normalizationIn)
normalizationIn
- the type of normalization to be applied to the
transformed datapublic double[] transform(double[] f, TransformType type)
transform
in interface RealTransformer
f
- 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)
transform
in interface RealTransformer
f
- 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)
f
- the real data array to be transformedMathIllegalArgumentException
- if the length of the data array is
not a power of two plus oneCopyright © 2019 CNES. All rights reserved.