Introduction to Wavelet Theory

Time-series data owes its name to its data points being a function of time. If this function is sufficiently well-behaved, it can be alternatively represented as a Wavelet Series.

What is a Wavelet Series?

Signals bear representation in both the time and frequency domains.

Time and Frequency Domain Representations of a Signal

Wavelet Transforms decompose a signal at multiple resolutions, and thus convey information from both the time and frequency domain:

Dyadic Time-Frequency Tiling

In this tutorial, we will be using the Discrete Wavelet Transform with the Haar Basis Function:

The Haar Transform

One advantage of using the DWT with the Haar Basis Function is that the computational complexity is only linear: O(n).

One disadvantage is that, as a discrete wavelet transform, frequency localization is poor.

In the next tutorial, I will show you how to perform the Discrete Wavelet Transformation on Financial Time-Series Data from Quandl with Python.

Thanks!