Discussing the article: "Filtering and feature extraction in the frequency domain"

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Check out the new article: Filtering and feature extraction in the frequency domain.

In this article we explore the application of digital filters on time series represented in the frequency domain so as to extract unique features that may be useful to prediction models.

In the article "Practical Implementation of Digital Filters in MQL5 for Beginners" the author, presented  digital filters applied in the time domain, through convolution. The series is multiplied with a unique set of weights of varying length, depending on the filter type and its parameters. The number of weights define a moving window that is convolved with corresponding series values as the filter is applied over the extent of the data. Moving averages also work in the same manner.

In this article, we will apply filters in the frequency domain. The basic steps involved are as follows:

1.  First the series is preprocessed in preparation of a DFT operation.
2.  The DFT is applied to the series using the Fast Fourier Transfrom algorithm (FFT).
3.  Next we manipulate the waveform of the series in whatever way we deem necessary. That is to say, a filter is applied, thereby modifying the original waveform of the series.
4.  An inverse DFT operation is done on the modified waveform, converting it back to the familiar time domain.
5.  Lastly we undo any effects brought on by operations conducted at the initial preprocessing step.

Author: Francis Dube