## Ehlers Filters

To affinity and beyond Buzz Lightyear (paraphrased) The most common filters used by traders are moving averages either Simple Moving Averages (SMA) or Exponential Moving Averages (EMA). These are linear filters. Linear filters are optimal for smoothing stationary, slowly varying signals that are corrupted with high-frequency noise. Unfortunately, price data are not stationary much of the time. A coin flip experiment is an example of a statistical stationary process. However, if weighted coins...

## What You See Is What You

Success is a journey, not a destination. That famous half-glass of water optimists see it as half-full and pessimists see it as half-empty. An engineer sees the glass as having been designed with too much capacity. That which we see is really a matter of perception. Market technicians have designed a wide variety of techniques to visualize what has happened in the past in order to infer what the future holds. Candlestick charts and Point and Figure charts are two examples of charting price...

## Z Transform

Just as Laplace and Fourier Transforms are powerful tools for continuous systems, Z Transforms provide a corresponding powerful tool for discrete systems. There are significant parallels between Z Transforms and Fourier Transforms. The Z Transform can be multiplied by the transfer response of a system to obtain a Z Transform of the system output. The sampled data output for a discrete system can be found by taking the inverse Z Transform. Because this theory is so important to digital signal...

## Key Point lo Remember

A um the irwirlcfet i in a Trtnd Modi p iiie cri lia arc met. A Cycle Modeexists ior 3 hnlf-douiiiwitt cycle aher the cm ins oi the Si new ivc Indicator lines or vhen the aieasv pKi c raie oi change is within 50 percent of the pb.isc of change irf tlve dominant cycle. A Trend Mode is declared if ihe 4-bar WMA i s paraccd the Instantaneous 'I endline by mour tliao 1.5 percent. The market mode can be iden i ified as a yw ntbair or uao lt i as c kle iraj menr in in automatic Leading system....

## Finite Impulse Response Filters

There is nothing permanent except change. A Simple Moving Average SMA is one example of a Finite Impulse Response FIR filter. Spoken, these filters are alternatively pronounced eff-eye-are or fur filters. FIR filters have no corollary in the physical world they exist only as digital computations. Their unique characteristic is that their impulse response is exactly the same as their coefficients. An impulse as input digital data is simply unity for one sample and zero for all other samples. As...

## Moving Averages

Lewis Mumford Centuries ago Karl Friedrich Gauss proved that the average is the best estimator of the random variable. He derived the familiar bell-shaped probability density curve known as the Gaussian, or Normal, distribution. When the probability distribution of a random variable is unknown the Gaussian distribution is generally assumed. In this bell-shaped curve, the peak value, or the mean, is the nominal forecast. The width of the variation from the mean is described...

## Signaltonoise Ratio

Logic is a system whereby one may go wrong with confidence. The signal amplitude is simply the length of the phasor. Recalling the Pythagorean Theorem, the length of the phasor is the square root of the sum of the squares of the InPhase and Quadrature components. We therefore have the signal amplitude on a bar-by-bar basis after we take the Hilbert Transform. The signal amplitude is not of much use by itself. However, if we can estimate the signal amplitude relative to the market noise, we then...

## Cycleperiod Dominant Cycle Half

Perhaps the term instantaneous is a bit presumptuous to apply to the concepts we discuss in this chapter. Nonetheless, the term is somewhat appropriate in that our technology enables us to compute a continuous trendline from which we can rapidly assess market action. As derived from the Drunkard's Walk problem in Chapter 1, our model says the market consists of a Trend Mode and a Cycle Mode. It is more accurate to describe the general market as a combination of these two modes. Furthermore, in...

## F The Sinewave Indicator

A painter can hang his pictures, but a writer can only hang himself. As noted in Chapter 6, the Hilbert Transform synthesizes the InPhase and Quadrature components from the analytic waveform. We can then immediately compute the phase of the signal by taking the arctangent of the ratio of these components. In principle, that should tell us where we are positioned within the cycle. Unfortunately, this is not true. The first problem is that the Hilbert Transform induces a lag of 7 bars. That lag...

## Introduction To The Science Of Digital Signal Analysis

Computet are worthless They can only jtrvc you answers Make no mistake bout it. This is a book for traders about digs-til signal processing It is not a book ior engineers about trading. At first glance, the reverse may seem to be true tor many traders because the subject matter is on the cutting edge of technology and the mathematics behind this technology can be more advanced than that encountered in school. Recognizing that many traders want to simply use the technology rather than become...

## Momentum Functions

Hack ward, turn backward, oh time w yuui flight. I can't begin to tell you the number ot traders that has asked me to make their signals happen just one bar sooner. The typical question is Can't you just take a momentum In the most simple case, momentum is just the 1-bar difference in pricc. Momentum is deceiving because it can give the illusion of anticipating turning points. In tact, there are cases in which some form of a momentum can increase the reaction time of an indicator. Even...

## Homodyne Discriminator

Dyne means we axe multiplying the signal by itself. More we want to multiply the signal of the current bar with _omplex conjugate of the signal 1 bar ago. The complex confabs, by definition, a complex number whose sign of the 'nary, component has been reversed. Expressing the signal lar coordinates, the arithmetic is pe Jipe'00-1 pV-K,- - gt pV The interesting result is that we get both the square of the sig-amplitude and the angular frequency lit Period from the ict because the difference in...