## Code Outline and Intuition

**The art of good trading is to be one step behind the market and two steps ahead of everybody else.**

__The Application of the Laplace Transform to Financial Markets ____Intuitional Steps.__** **

**The price axis is in log Pi as opposed to base 10.****T****his shows that all the booms and busts of the last century are related to each other by Pi and the square roots of Pi.**

**This is the last thing you would expect a random walk to do.****It is however the first thing you would expect a wave equation to do.**

**Money circulates therefore its internal dynamics are circular in nature.****They are polar functions and are measured in radians per unit time.****This makes numeric analysis on the complex plane possible.**

**This is what W.D. Gann’s was doing with his various wheels.****There is however a far easier way to do it, by rearranging the question and using differential calculus to solve it.**

**To do this you need to know the general form of the underlying integral equation of the market.****The compound interest rate function is at the heart of all monetary systems.****Which you integrate and convolute with the market to integrate out time from price altogether.**

**To reveal the directions and magnitudes of the underlying wave functions of the long term carrier waves / swings in the market.****Which you can then solve algebraically for a trading solution using an exponential step controller to regulate a discrete trading signal.****This returns a process control solution that switches when the major changes in real time.**

__The Process Controller.____ __

**To regulate the output of the system you have employ an escapement mechanism that prevents the function from constantly over running the market and creating false signals.****It is all but identical to the mechanism that stops clock spring from releasing all its energy at once.****To capture the energy of an irregular out of balance oscillation with the objective of damping out the short term oscillations / swings and capturing the energy of the long term swings.**

**To reveal the true state of play in the major trend as it happens in real time without the phase delay and false signals of moving averages****So when the market goes sideways so do integral contour functions of your signal whereas moving averages converge to the price and generate false signals and lots of them.****If you keep the change natural log of the price as a as a cumulative time series**

**You can then do your signal processing using linear algebra.****With a tri state logic output to solve for the direction of underlying trend in real time.**

__Function Outline:____ __**S is constant typically 10^-1 < S < 10^.
**

**Es(0) = Ln(Close);****Es(1) = Es(0) + Ln(Close1) – Ln(Close0);****Es(2) = Es(1) + Ln(Close2) – Ln(Close1);**

**Fs(t) = if(|dEs(t)| > S) Fs(t) += Fs(t+1) + jS;****j = Ln(Close1) – Fs(n-1) / | Ln(Close1) – Fs(t+1) |;**

**Js(t) = Fs(t) – Fs(t-1) / | Fs(t) – Fs(t-1) |;****Hs(n) = Js(t) – Js(t-1) / | Js(t) – Js(t-1) |;**

__Coding Outline:
__

**Function Inputs****Time****The last market price****The value of S.****The order of magnitude S.****The Z axis Resolution Step**

**Data Structures.**

**The incoming market data****The integrations of the market prices.****The exponential unit step controller.**

**The outputs are.**

**The market chart contour.****The Fringe magnitudes****The Poisson distribution of the signal****The market signal the center line of the Poisson distribution****The filtered / rectified return market signal.**

** **__Contour Processing.
__

**The method is to create a time series of the differences between a known differential equation / contour and the market you are tracking as a complex number.**

**You can do this by using an exponential step controller that ignores the passage of time and simply looks at the unit step change in price.**

**If the distance is greater that a specific value it take one unit step in up or down depending on the direction of the market.**

**When a change in trend is detected steps in the other direction.**

**Each contour is tracking the one before it.**

**Signal Processing is done by taking the sum of the directions of all the contours and plotting it as a Poisson / Bernoulli count distribution.**

**This returns the magnitude of the underlying trend as a stepped ramp function and a tri state logic signal -1 0 1.**