gsignal (version 0.3-1)

welchwin: Welch window

Description

Return the filter coefficients of a Welch window of length n.

Usage

welchwin(n, method = c("symmetric", "periodic"))

Arguments

n

Window length, specified as a positive integer.

method

Character string. Window sampling method, specified as:

"symmetric"

(Default). Use this option when using windows for filter design.

"periodic"

This option is useful for spectral analysis because it enables a windowed signal to have the perfect periodic extension implicit in the discrete Fourier transform. When 'periodic' is specified, the function computes a window of length n + 1 and returns the first n points.

Value

Welch window, returned as a vector.

Details

The Welch window is a polynomial window consisting of a single parabolic section: $$w(k) = 1 - (k / N - 1)^2, n=0,1, ... n-1$$. The optional argument specifies a "symmetric" window (the default) or a "periodic" window. A symmetric window has zero at each end and maximum in the middle, and the length must be an integer greater than 2. The variable N in the formula above is (n-1)/2. A periodic window wraps around the cyclic interval 0,1, ... m-1, and is intended for use with the DFT. The length must be an integer greater than 1. The variable N in the formula above is n/2.

Examples

# NOT RUN {
w <- welchwin(64)
plot (w, type = "l", xlab = "Samples", ylab =" Amplitude")

ws = welchwin(64,'symmetric')
wp = welchwin(63,'periodic')
plot (ws, type = "l", xlab = "Samples", ylab =" Amplitude")
lines(wp, col="red")

# }