KernelWeight is an S4 class that implements a weighting function by
specification of a kernel function W and a scale parameter bw.
Wa kernel function
bwbandwidth
envAn environment to allow for slots which need to be accessable in a call-by-reference manner:
valuesA vector storing the weights; see the Details section.
WnjA vector storing the terms used for normalization; see the Details section.
It extends the class Weight and writes
$$W_N(2\pi (k-1)/N) := \sum_{j \in Z} bw^{-1} W(2\pi bw^{-1} [(k-1)/N + j])$$
to values[k] [nested inside env] for k=1,...,N.
The number length(values) of Fourier frequencies for which
\(W_N\) will be evaluated may be set on construction or updated when
evoking the method getValues.
To standardize the weights used in the convolution to unity
$$W_N^j := \sum_{j \neq s = 0}^{N-1} W_n(2\pi s / N)$$
is stored to Wnj[s] for s=1,...,N, for later usage.
Brillinger, D. R. (1975). Time Series: Data Analysis and Theory. Holt, Rinehart and Winston, Inc., New York. [cf. p. 146 f.]
Examples for implementations of kernels W can be found at:
kernels.