window_symm: 1D Symmetric Window Functions.

In CovEsts: Nonparametric Estimators for Covariance Functions

1D Symmetric Window Functions.

Description

A symmetric window function in this context are traditional window functions, unlike the window functions. This computes one of the symmetric window functions listed below, all of which are defined for x \in [-1, 1], and are 0 otherwise.

Usage

window_symm(x, name, params = c(1))

Arguments

x	A vector or matrix of arguments of at least length 1. Each value must be between 0 and 1, inclusive.
name	The name of the window. Options are: tukey, triangular, sine, power_sine, blackman, hann_poisson, welch.
params	A vector of parameters for the windows. See the documentation below for the position of the parameters.

Details

Tukey Window. The Tukey window is defined as

w(x) = \frac{1}{2} + \frac{1}{2} \cos(\pi |x|) , x \in [-1, 1].

The params argument is empty, see the example.

Triangular Window. The triangular window is given by

w(x) = 1 - |x|, x \in [-1, 1].

The params argument is empty, see the example.

Sine Window. The sine window is given by

w(x) = 1 - \sin\left(\pi |x| / 2 \right), x \in [-1, 1].

The params argument is empty, see the example.

Power Sine Window. The power sine window is given by

w(x; a) = 1 - \sin^{a}(\pi |x| / 2), x \in [-1, 1], a > 0.

The params argument is of the form c(a)

Blackman Window. The Blackman window is defined as

w(x; a) = 1 + ( (a - 1) / 2) + \frac{1}{2} \cos(\pi |x|) - \frac{a}{2} \cos(2 \pi |x|), x \in [-1, 1], a \in {R} .

The params argument is of the form c(a). The standard value of a for this window is 0.16.

Hann-Poisson Window. The Hann-Poisson window is defined as

w(x; a) = 1 - \frac{1}{2} (1 - \cos(\pi |x|)) \exp( - (a \left|1 - |x| \right|) ) , x \in [-1, 1], a \in {R} .

The params argument is of the form c(a)

Welch Window. The Welch window is given by

w(x) = (|x| - 1)^2 , x \in [-1, 1] .

The params argument is empty, see the example.

Value

A vector or matrix of values.

Examples

x <- c(-0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6)
window_symm(x, "tukey")
window_symm(x, "triangular")
window_symm(x, "sine")
window_symm(x, "power_sine", c(0.7))
window_symm(x, "blackman", c(0.16))
window_symm(x, "hann_poisson", c(0.7))
window_symm(x, "welch")
curve(window_symm(x, "tukey"), from = -1, to = 1)
curve(window_symm(x, "triangular"), from = -1, to = 1)
curve(window_symm(x, "sine"), from = -1, to = 1)
curve(window_symm(x, "power_sine", c(0.7)), from = -1, to = 1)
curve(window_symm(x, "blackman", c(0.16)), from = -1, to = 1)
curve(window_symm(x, "hann_poisson", c(0.7)), from = -1, to = 1)
curve(window_symm(x, "welch"), from = -1, to = 1)

CovEsts documentation built on Sept. 10, 2025, 10:39 a.m.