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.
| Modifier and Type | Field and Description |
|---|---|
| private final DctNormalization | normalization
The type of DCT to be performed. |
| pack-priv static final long | serialVersionUID
Serializable version identifier. |
| Access | Constructor and Description |
|---|---|
| public | FastCosineTransformer(final DctNormalization
the type of normalization to be applied to the
transformed data normalization)Creates a new instance of this class, with various normalization conventions. |
| Modifier and Type | Method and Description |
|---|---|
| protected double[] | Returns: the real transformed arraythe real data array to be transformed f)Perform the FCT algorithm (including inverse). |
| public double[] | transform(final double[]
the real data array to be transformed (signal) f, final TransformType the type of transform (forward, inverse) to be performed type)Implements org. Returns the (forward, inverse) transform of the specified real data set. |
| public double[] | transform(final UnivariateFunction
the function to be sampled and transformed f, final double the (inclusive) lower bound for the interval min, final double the (exclusive) upper bound for the interval max, final int the number of sample points n, final TransformType the type of transform (forward, inverse) to be performed type)Implements org. Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval. |
| normalization | back to summary |
|---|---|
| private final DctNormalization normalization The type of DCT to be performed. | |
| serialVersionUID | back to summary |
|---|---|
| pack-priv static final long serialVersionUID Serializable version identifier. | |
| FastCosineTransformer | back to summary |
|---|---|
| public FastCosineTransformer(final DctNormalization normalization) Creates a new instance of this class, with various normalization conventions.
| |
| fct | back to summary |
|---|---|
| protected double[] fct(double[] f) throws MathIllegalArgumentException Perform the FCT algorithm (including inverse).
| |
| transform | back to summary |
|---|---|
| public double[] transform(final double[] f, final TransformType type) throws MathIllegalArgumentException Implements org. Doc from org. Returns the (forward, inverse) transform of the specified real data set.
| |
| transform | back to summary |
|---|---|
| public double[] transform(final UnivariateFunction f, final double min, final double max, final int n, final TransformType type) throws MathIllegalArgumentException Implements org. Doc from org. Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
| |