Instantaneous Trend Line: Removing the Dominant Cycle with a Period Average

Summary

This note explains the idea behind John Ehlers’ Instantaneous Trend Line. It argues that a simple moving average spanning the dominant cycle can cancel much of that cycle: samples above and below the midpoint balance across a full cycle. In frequency terms, the rectangular averaging window has a sinc-shaped response, with a null placed at the cycle period.

The described version changes the original indicator’s parameterization. It uses a period input rather than a fractional alpha, making the control resemble the period used for other averages. The note gives a conceptual and mathematical rationale, but no formula, implementation details, market examples, or performance tests. Its usefulness therefore lies in understanding the filtering intuition and the revised input convention; it does not establish that the indicator predicts price direction or improves trading results.

Key ideas

• The indicator aims to suppress the dominant cycle by averaging across its full period.
• A full-cycle average can balance observations above and below the midpoint.
• The rectangular averaging window has a sinc frequency response with a null at the selected cycle.
• This generalized version uses a period parameter instead of a fractional alpha.
• The note provides a rationale but no implementation, examples, or performance evidence.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.