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.
Wavelet Transforms decompose a signal at multiple resolutions, and thus convey information from both the time and frequency domain:
In this tutorial, we will be using the Discrete Wavelet Transform with the Haar Basis Function:
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!