Main difference of FTLM and STLM from classical technical instrument Momentum is that for its calculation not the close prices but smoothed (leveled) in the result of filtration values of the trend line are used. In the result FTLM and STLM turn out more leveled (smoothed) and regular functions than the classical instrument Momentum, and therefore have more forecasting value.

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What is the filter?

In signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.

Ok. Why digital?

A digital filter uses a digital processor to perform numerical calculations on sampled values of the signal. The processor may be a general-purpose computer such as a PC, or a specialized DSP (Digital Signal Processor) chip.

Too complicated. Do I know the filter?

Yes of course:

- Simple Moving Average (SMA) is a average value of a last sequence in series of data. It is an example DF with Finite Impulse Response FIR also known as non-recursive filters.

- Triangle and Weighted Moving Average are calculated as SMA but elements in the series have different weights. Triangle (TMA) has maximum weight in the middle. Weighted (WMA) has minimum weights in the middle.

- Exponential MA is calculated as: Y = Y + (X - Y) * Alpha Where X is input data. Y is output data. Alpha is a coefficient that defines the smoothness of the indicator line. This is an example of DF as IIR filter.

- Momentum, ROC, MACD, TRIX and others - digital filters as well.

So what we are talking about! We know those filters!

Most of indicators used in Technical Analysis (TA) are regular linear digital filters (DF). Practically all of them have inside themselves moving averages parts (which are low pass filters). We can say now that the DF is a part of any TA. DFs are well investigated. There are methods of calculating of DF by calculatios, by weights coefficients or by the impulse response.