Inverse Fisher Transform

What is the Inverse Fisher Transform?

The Inverse Fisher Transform is John Ehlers' recipe for making an oscillator's output more decisive. It runs a zero-centered input through (e^(2x) - 1) / (e^(2x) + 1), which is algebraically the hyperbolic tangent: an S-curve that compresses everything into -1 to +1. The curve is nearly linear for small inputs, but moderately strong inputs get pushed hard toward the rails, so with the input scaled sensibly the transformed oscillator spends most of its time saturated near an extreme and crosses the middle quickly.

Ehlers' published example applied it to RSI: center a short RSI on zero, scale it down, smooth it with a weighted moving average, then transform, with crossings of ±0.5 as the conventional triggers. It is the counterpart of the Fisher Transform, which stretches tails to sharpen extremes; the inverse compresses them to create clean, nearly binary states.

How traders use it

• As a signal cleaner: applied to RSI, stochastics, or the Stochastic Momentum Index, it converts fuzzy overbought/oversold territory into saturated states, with the cross up through -0.5 and down through +0.5 as the standard triggers.
• As a compact regime flag: because the output sits near +1 or -1 most of the time, it summarizes an oscillator's state cleanly for dashboards, screeners, and multi-timeframe panels.
• As a normalization stage: it is one of the sigmoid-style transforms used to squash inputs into a fixed range before combining or thresholding signals.