Filtering
Introduction
Filtering in a broad sense, is a method of removing any unwanted quantity from a mixture of the desired quantity and the undesired quantity. In the world of signals, this generally applies to the process of either separating different channels of a signal, or removing a noise signal to get the original signal.
This usually makes more sense when we talk about something real. Say, music, or images, or surprisingly, even the stock market! That's right. It is possible, from simple spectral analysis to "filter" out long-term and short term trends from any time varying data. This includes weather, astronomical events, and pretty much any time-varying signal you can think of.
Simple Example
- I always like to start with out our friendly sine wave. After all, that is what Fourier started with too.
- So, what we do is start by taking a clean sine wave from -$ -\pi to \pi $
- To the sine wave, we add some pretty ugly Gaussian noise, shown above.
- What results is a much noisier signal, as can be clearly seen.
