The MacGyver Of Indicators
Swiss Army Knife Indicator

by John F. Ehlers

You've probably never heard of this indicator, but it has all the common functions such as smoothing and momentum generation. Find out why it's going to be your new best friend.

This indicator does some unusual things, such as band-stop and band reject filtering. Once you program this indicator into your trading platform, you can perform virtually any technical analysis technique with it. This unique general indicator results from general digital signal processing (DSP) concepts for discrete signal networks that appear in various forms in technical analysis.

Z-TRANSFORMS

The description of this indicator involves Z-transforms. Z-transforms are a convenient way of solving difficult difference equations in much the same way that LaPlace transforms are used to solve differential equations in calculus. Difference equations arise from the use of sampled data, the way we have in technical analysis: Daily bars sample price data once a day. Intraday bars sample price data every minute, hour, or whatever. The concept is the same regardless of the sampling rate. In Z-transforms, Z-1 stands for one sample period of delay. For simplicity, I will always refer to daily bars as the sample rate.

The transfer function of a discrete linear system is the ratio of the output of the system divided by the input. Since both the output and input can be described in terms of polynomials in the Z domain, we can write the transfer function of a very simple indicator as:

In this case, both the input and output involve only a constant term and a term having one unit of delay. By cross-multiplying and factoring, we can describe the output in terms of the input as:

This equation is easily converted to indicator programming languages. For example, in EasyLanguage, N units of delay is noted as [N] after the variable. Thus, the transfer function programs to:

...Continued in the January 2006 issue of Technical Analysis of STOCKS & COMMODITIES

Excerpted from an article originally published in the January 2006 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 2005, Technical Analysis, Inc.