Constructing a Hilbert squelch dominant-cycle gate

Start from a spectral period meter

Spectral analysis, in this construction, means recovering a time-varying cycle length from in-phase and quadrature components of an ordered price series rather than from a fixed lookback oscillator.

The dominant cycle is the bar length implied by accumulating successive phase increments until they complete one full rotation.

The default input to the in-phase and quadrature extraction is mid-price, formed as the average of each bar high and low.

Form a phase angle from in-phase and quadrature

In-phase is the recursively smoothed even-symmetric component taken from lagged mid-price differences.

Quadrature is the recursively smoothed odd-symmetric companion component used with in-phase to form a phase angle.

Those components are converted to a phase angle with an arctangent, and quadrant rules expand that arctangent into a 360-degree phase reading.

Accumulate clipped increments to a period

Successive phase changes are wraparound-corrected and then clipped so each increment stays between 1 and 60 degrees.

The instantaneous period is the lookback count at which clipped phase increments first sum to a full circle. In the archive workflow that count is the bar count at which the increments first accumulate to 360 degrees, searched over a window of up to 40 increments, and it is taken before optional smoothing.

A missing instantaneous estimate is replaced by the prior value, and the published period is 0.25 times the new estimate plus 0.75 times the previous smoothed period.

Install the squelch-threshold

A default squelch cutoff of 20 marks bars whose smoothed period is shorter than that cutoff.

The squelch-threshold is the minimum accepted period. Readings shorter than this cutoff are treated as a separate regime from cycle mode.

Implementations use that period-versus-cutoff test to label bars as trend mode or cycle mode. Trend mode is the regime flag used when the smoothed period is below the squelch cutoff. Cycle mode is the regime flag used when the smoothed period is at or above the squelch cutoff.

Feed a display or a later model input

The below-cutoff condition is rendered as a chart highlight or recoded as a 1/0 stream so the same construction can feed a display or a later model input.