Fourier-transform for Time-Sequence: Detrending | by Yoann Mocquin | Aug, 2023

Detrending your time-series may be a game-changer

Detrending a sign earlier than computing its Fourier remodel is a typical apply, particularly when coping with time-series.

On this put up, I wish to present each mathematically and visually how detrending your sign impacts its Fourier-transform.

All pictures by writer.

This put up is the fourth of my Fourier-transform for time-series sequence: I take advantage of quite simple examples and some mathematical formulation to elucidate varied ideas of the Fourier remodel. You don’t have to learn them within the order under, I’d fairly advocate going forwards and backwards between every article.

Try the earlier posts right here:

  • Overview how the convolution relate to the Fourier remodel and how briskly it’s:
  • Deepen your understanding of convolution utilizing picture examples:
  • Perceive how the Fourier-transform might be visualy understood utilizing a vector-visual strategy:

On this put up, we’re going to discover 2 sorts of detrends : we’ll name them ‘fixed’ and ‘linear’ detrendings.

The tip objective of this put up is to make you perceive what are fixed and linear detrending, why we use them, and the way they impacts the Fourier-transform of the sign.

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