> For the complete documentation index, see [llms.txt](https://zavalab.gitbook.io/statschemebook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://zavalab.gitbook.io/statschemebook/chapter-6-statistical-data-analysis-and-learning/01-signal-processing.md).

# Part II: Signal Processing

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**Slides:** [stats\_ch6\_partII.pdf](https://github.com/vzavala/StatsBook/blob/master/Slides/stats_ch6_partII.pdf) · [4-up handout](https://github.com/vzavala/StatsBook/blob/master/Slides/handouts/stats_ch6_partII_4up.pdf) · **Code:** [Python notebooks](https://github.com/vzavala/StatsBook/tree/master/Python) · [MATLAB scripts](https://github.com/vzavala/StatsBook/tree/master/Matlab) · [MATLAB live scripts](https://github.com/vzavala/StatsBook/tree/master/Matlab-Live)
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* Signal processing (SP) is a field of mathematics that provides tools for analyzing, modifying, and synthesizing data.
* Data often appears as temporal signals (e.g., temperature, vibration, sound) or spatial signals (e.g., images, tomography, micrographs).
* We look into an SP task known as filtering (removes unwanted features from data) with goal of extracting dominant features (patterns).
* Filtering is a powerful way to preprocess raw data and can be beneficial in performing estimation, modeling, and data analysis.
* *Convolution* is fundamental operation behind filtering. This is a *weighted sum of data points* over local subdomain (window) of signal.
* *Fourier transform* is another fundamental operation of SP that transforms data to frequency domain; this facilitates convolution and allows us to characterize features in terms of frequency content.
* Features extracted from convolutions can be used to classify images; this is basic principle behind machine learning techniques such as convolutional neural nets.