Window Functions

Available windowing functions for use in Fourier transforms

Note: Most of the following functions assume an input range of $0 \leq x \leq 1$ .

Keyword	Parameters	Description
`None`	–	No window function
`Bartlett`	–	Bartlett (triangular) window $f (x) = \frac{\| x - 0.5 \|}{0.5}$
`Hann`	–	von Hann (Hanning) window $f (x) = \frac{1}{2} (1 - \cos (2 π x))$
`Lanczos`	–	Lanczos window $f (x) = \frac{\sin (π (2 x - 1))}{π (2 x - 1)}$
`Nuttall`	–	Nuttall window (continuous first derivatives over range) $f (x) = 0.355768 - 0.487396 \cos (2 π x) + 0.144232 \cos (4 π x) - 0.012604 \cos (6 π x)$
`Sine`	–	Sine Window $f (x) = 1 - \sin (\frac{1}{2} π x)$
`Lorch0`	–	Original Lorch function - $x$ here represents the real value of the current position, rather than one converted to the range $0 \leq x \leq 1$ . $f (x) = \frac{\sin (x Δ_{0})}{x Δ_{0}}, Δ_{0} = \frac{p i}{x_{m a x}}$

Last modified February 24, 2023: Docs 1.0 (#1221) (6f6c04b7e)