Class FastCosineTransformer
- All Implemented Interfaces:
Serializable
,RealTransformer
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
- xk# = xk if 0 ≤ k < N,
- xk# = x2N-2-k if N ≤ k < 2N - 2.
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.
- See Also:
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Constructor Summary
ConstructorDescriptionFastCosineTransformer
(DctNormalization normalization) Creates a new instance of this class, with various normalization conventions. -
Method Summary
Modifier and TypeMethodDescriptionprotected 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.
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Constructor Details
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FastCosineTransformer
Creates a new instance of this class, with various normalization conventions.- Parameters:
normalization
- the type of normalization to be applied to the transformed data
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Method Details
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transform
Returns the (forward, inverse) transform of the specified real data set.- Specified by:
transform
in interfaceRealTransformer
- 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
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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 interfaceRealTransformer
- Parameters:
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 performed- Returns:
- the real transformed array
- Throws:
MathIllegalArgumentException
- if the lower bound is greater than, or equal to the upper boundMathIllegalArgumentException
- if the number of sample points is negativeMathIllegalArgumentException
- if the number of sample points is not a power of two plus one
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fct
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
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