How Does the Uncertainty Principle Limit Time Series Analysis?

Why we can’t extract precise time and frequency information from a time series mutually, and how wavelet analysis can tackle this limitation

1. Introduction

The connection between the Fourier Transform, Uncertainty Principle, and time series analysis unveils a fascinating interplay that shapes the extraction of simultaneous temporal and frequency information. To understand this relationship, it's important to first briefly understand what a Fourier Transform (FT) and the uncertainty principle are as a consequence. Then, …

data science fourier-transform timeseries time-series-analysis