# KernelWeight-class: Class for Brillinger-type Kernel weights.

### Description

KernelWeight is an S4 class that implements a weighting function by specification of a kernel function W and a scale parameter bw.

### Details

It extends the class Weight and writes

W_N(2π (k-1)/N) := ∑_{j \in Z} bw^{-1} W(2π 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 := ∑_{j \neq s = 0}^{N-1} W_n(2π s / N)

is stored to Wnj[s] for s=1,...,N, for later usage.

### Slots

W

a kernel function

bw

bandwidth

env

An environment to allow for slots which need to be accessable in a call-by-reference manner:

values

A vector storing the weights; see the Details section.

Wnj

A vector storing the terms used for normalization; see the Details section.

### References

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.