public class FastSineTransformer extends Object implements RealTransformer, Serializable
There are several variants of the discrete sine transform. The present
implementation corresponds to DST-I, with various normalization conventions,
which are specified by the parameter DstNormalization.
It should be noted that regardless to the convention, the first
element of the dataset to be transformed must be zero.
DST-I is equivalent to DFT of an odd extension of the data series. More precisely, if x0, …, xN-1 is the data set to be sine transformed, the extended data set x0#, …, x2N-1# is defined as follows
Then, the standard DST-I y0, …, yN-1 of the real
data set x0, …, xN-1 is equal to half
of i (the pure imaginary number) times the N first elements of the DFT of the
extended data set x0#, …,
x2N-1#
yn = (i / 2) ∑k=02N-1
xk# exp[-2πi nk / (2N)]
k = 0, …, N-1.
The present implementation of the discrete sine transform as a fast sine
transform requires the length of the data to be a power of two. Besides,
it implicitly assumes that the sampled function is odd. In particular, the
first element of the data set must be 0, which is enforced in
transform(UnivariateFunction, double, double, int, TransformType),
after sampling.
| Constructor and Description |
|---|
FastSineTransformer(DstNormalization normalization)
Creates a new instance of this class, with various normalization conventions.
|
| Modifier and Type | Method and Description |
|---|---|
protected double[] |
fst(double[] f)
Perform the FST 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 FastSineTransformer(DstNormalization normalization)
normalization - the type of normalization to be applied to the transformed datapublic double[] transform(double[] f,
TransformType type)
0.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, or the first element of the data array is not zeropublic double[] transform(UnivariateFunction f, double min, double max, int n, TransformType type)
f(x) = 0.0 at x = 0.0.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 twoprotected double[] fst(double[] f)
throws MathIllegalArgumentException
0.f - the real data array to be transformedMathIllegalArgumentException - if the length of the data array is
not a power of two, or the first element of the data array is not zeroCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.