The Hilbert Transform is a technique used to generate inphase and quadrature components of a de-trended real-valued "analytic-like" signal (such as a Price Series) in order to analyze variations of the instantaneous phase and amplitude.. HTDCPhase returns the Hilbert Transform Phase of the Dominant Cycle. The Dominant Cycle Phase lies in the range of 0 to 360 degrees. The Hilbert Transform Lead Sine is just the sine of the DC Phase advanced by 45 degrees. The DC Phase at a specific bar gives the phase position from 0 to 360 degrees within the current Hilbert Transform Period instantaneously measured at that bar. The HTLeadSin is the sine of the DC Phase at a specific bar. It is most often used in conjunction with the HTSin indicator to identify cyclic turning points. Quoting from Market Mode Strategies.doc by John Ehlers from MESA Software, "A clear, unequivocal cycle mode indicator can be generated by plotting the Sine of the measured phase angle advanced by 45 degrees. This leading signal crosses the sinewave 1/8th of a cycle BEFORE the peaks and valleys of the cyclic turning points, enabling you to make your trading decision in time to profit from the entire amplitude swing of the cycle. A significant additional advantage is that the two indicator lines don't cross except at cyclic turning points, avoiding the false whipsaw signals of most "oscillators" when the market is in a Trend Mode. The two lines don't cross because the phase rate of change is nearly zero in a trend mode. Since the phase is not changing, the two lines separated by 45 degrees in phase never get the opportunity to cross." See the examples.
