## audacity-nyquist

 [Audacity-nyquist] Nonlinear Expander ATanh - Nyquist plugin for Audacity From: Igor Chernenko - 2008-12-04 03:57:59 Attachments: atanh - decompression curve - expand 1.0.png Nonlinear-Expander-atanh.ny ```Nonlinear Expander ATanh - Nyquist plugin for Audacity File: "Nonlinear-Expander-atanh.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 , you can decompress it with ; HOW IT WORKS ; ; Nonlinear Expander ATanh performs smooth non-linear 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 ; ; Edgar-RFT: Logarithmic math with Nyquist and XLISP ; http://n2.nabble.com/plugin:-distortion-via-nth-root-function-td238782.html ```