**Signal Processing Using Trend Decomposition**

June 13, 2017

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Signal processing is the process of using a computer for numerical calculations. Multiple algorithms have been created that improve the process of identifying signals. Though computer capability have increased, humans are necessary to manipulate algorithms so they can be efficiently implemented. We implement these techniques to find patterns in the future movements of financial securities. Below we will describe the use of TD in pattern recognition.

Trend decomposition (TD) is a nonlinear signal- transformation method developed by Huang et al. (1998, 1999). It is used to decompose a nonlinear and non-stationary time series into a sum of intrinsic mode function (IMF) components with individual intrinsic time scale properties.

IMF must satisfy the following two conditions:

1.) The number of extreme values and zero-crossings either are equal or differ at the most by one.

2.) The mean value of the envelope constructed by the local maxima and minima is zero at any point .

Procedure