Stochastic Signal Analysis is a field of science concerned with the processing, modification and analysis of (stochastic) signals.
Anyone with a background in Physics or Engineering knows to some degree about signal analysis techniques, what these technique are and how they can be used to analyze, model and classify signals.
Data Scientists coming from a different fields, like Computer Science or Statistics, might not be aware of the analytical power these techniques bring with them.
In this blog post, we will have a look at how we can use Stochastic Signal Analysis techniques, in combination with traditional Machine Learning Classifiers for accurate classification and modelling of time-series and signals.
At the end of the blog-post you should be able understand the various signal-processing techniques which can be used to retrieve features from signals and be able to classify ECG signals (and even identify a personby their ECG signal), predict seizures from EEG signals, classify and identify targets in radar signals, identify patients with neuropathy or myopathyetc from EMG signals by using the FFT, etc etc.
In this blog-post we’ll discuss the following topics:
- Basics of Signals
- Transformations between time- and frequency-domain by means of FFT, PSD and autocorrelation.
- Statistical parameter estimation and feature extraction
- Example dataset: Classification of human activity
- Extracting features from all signals in the training and test set
- Classification with (traditional) Scikit-learn classifiers
- Finals words
1. Basics of Signals
1.1 Signals vs Time-Series
You might often have come across the words time-series and signals describing datasets and it might not be clear what the exact difference between them is.
In a time-series dataset the to-be-predicted value () is a function of time (). Such a function can describe anything, from the value of bitcoin or a specific stock over time, to fish population over time. A signal is a more general version of this where the dependent variable does not have to a function of time; it can be a function of spatial coordinates (), distance from the source ( ), etc etc.
Signals can come in many different forms and shapes: you can think of audio signals, pictures, video signals, geophysical signals (seismic data), sonar and radar data and medical signals (EEG, ECG, EMG).
- A picture can be seen as a signal which contains information about the brightness of the three colors (RGB) across the two spatial dimensions.
- Sonar signals give information about an acoustic pressure field as a function of time and the three spatial dimensions.
- Radar signals do the same thing for electromagnetic waves.
In essence, almost anything can be interpreted as a signal as long as it carries information within itself.
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