Nonlinear Expander ATanh  Nyquist plugin for Audacity
File: "NonlinearExpanderatanh.ny" (in the attachment)
The purpose of Nonlinear Expander ATanh is to reduce loudness.
It can also perform exact decompression of sound compressed
with Nonlinear Maximizer Tahn. If, for example, your wave was
compressed with <maximize = 2.0>, you can decompress it with <expand = 2.0>
; HOW IT WORKS
;
; Nonlinear Expander ATanh performs smooth nonlinear transformation
of the sound.
; The result of this transformation is what is tend to be called expansion or
; decompression of the sound.
;
; The magic formula of decompression is hyperbolic arctangent:
;
; y = (1/k)*atanh(x*tanh(k)) [k > 0]
;
; x = sound
;
; y = decompressed sound
;
; atanh = hyperbolic arctangent
;
; tanh = hyperbolic tangent
; Nonlinear Expander ATanh is actually a reverse function of Nonlinear
Maximizer Tanh.
; This means that you can undo compression performed by Nonlinear
Maximizer Tanh,
; if you know the value of the compression parameter. This parameter
(k) is the same in
; both plugins, but it has two different names "expand" and
"maximize". The exact
; decompression requires "expand"="maximize".
; In the same way, you can undo "expansion".
;
; Wikipedia: Hyperbolic tangent, often pronounced "tanch" (or "than",
with the "th" like in "Thursday")
; http://en.wikipedia.org/wiki/Hyperbolic_function
; http://en.wikipedia.org/wiki/Math.h
;
; EdgarRFT: Logarithmic math with Nyquist and XLISP
; http://n2.nabble.com/plugin:distortionvianthrootfunctiontd238782.html
