Hilbert Transform

What is the Hilbert Transform?

The Hilbert transform is a signal-processing operation that shifts every frequency component of a series by 90 degrees. Pairing the original series with this shifted copy (the quadrature component) forms the analytic signal, from which two things can be read at every bar: instantaneous amplitude, the size of the current cycle, and instantaneous phase, the position within it. The rate at which phase advances is instantaneous frequency, and its inverse is the cycle period.

John Ehlers adapted the transform for trading with short filter approximations, making it the engine of the DSP school: dominant cycle measurement, phase tools like the sinewave indicator, and adaptive averages such as MAMA/FAMA that retune themselves to the measured period. The caveat: the math assumes a reasonably clean oscillation, which raw price is not, so implementations detrend and smooth first and still produce estimates that jitter around regime changes.

How traders use it

• To measure the dominant cycle period, which then drives adaptive lookbacks for oscillators and moving averages instead of fixed settings.
• To trade phase directly: phase-based tools anticipate cyclic turns as phase approaches its extremes, rather than waiting for a lagging crossover after the turn.
• To classify trend versus cycle mode: when measured phase stops advancing at the expected cycle rate, DSP systems switch from cycle tactics to trend tactics.