Taper
Description
Tapering consists of altering the ends of the (mean-adjusted) series so that they taper gradually down to zero.
An example of tapering is the TUKEY-HANNING Taper: the series is modified at the beginning at the end by means of a cosine transformation.
More exactly, if $\alpha$ is the proportion of the data being tapered, we have (using $l=\alpha n/2$):
\[x_i^{taper}=\begin{cases}0.5 x_i (1-\cos{ \pi i/l}) & i \lt l \\ 0.5 x_i (1-\cos{ \pi (n-i)/l}) & i \gt n-l \\ x_i & otherwise\end{cases}\]Implementation
The generic interface for tapers is demetra.data.ITaper
The TUKEY-HANNING Taper is implemeted in demetra.data.TukeyHanningTaper
double[] x=new double[60];
DataBlock X=DataBlock.ofInternal(x);
Random rnd=new Random();
X.set(rnd::nextGaussian);
TukeyHanningTaper taper=new TukeyHanningTaper(.5);
System.out.println(X);
taper.process(x);
System.out.println(X);
