A Pragmatic* Introduction to Signal Processing

 with applications in scientific measurement

An illustrated essay with free software and spreadsheet templates to download

Last updated  September 16, 2021.

A retirement project by Tom O'Haver , Professor Emeritus, Department of Chemistry and Biochemistry

Have a question or suggestion? E-mail me: toh@umd.edu. Join our group on Facebook

No cost, no
ads, no sign-in/registration, no eye candy, no cookies, no hype, no Java, no Flash, no kidding. Completely free since 1993.

This essay is also available as a 510-page printable document written in Microsoft Word and saved in
Word     and  PDF formats.
Readability index

The Kindle and paperback versions, ISBN: 979-8589799453, by Kindle Direct Publishing, are available from Amazon.

This entire web site can be downloaded in archived HTML format complete with all linked software (400 MBytes). 

  Check out the amazing feedback from users 

Introduction   Fourier deconvolution 
Signal arithmetic  Fourier filter 
Signals and noise  Wavelets and wavelet denoising
Smoothing  Integration and peak
area measurement 
Differentiation  Curve fitting A:
Linear Least Squares
Peak sharpening   Curve fitting B:
Multicomponent Spectroscopy 
Harmonic analysis 
Curve fitting C: Non-linear
Iterative Curve Fitting
Fourier convolution  A Combination of Methods

* Pragmatic: Relating to matters of fact or practical affairs, often to the exclusion of intellectual or artistic matters; practical as opposed to idealistic.

Appendix and Case Studies

The Animated Zoo of Tools and Demos 

 Catalog of downloadable software and templates

Interactive Signal Processing Tools for Matlab

Spreadsheets for Measurement Calibration

Peak Finding and
 Interactive Fourier Filter
Interactive Smoothing, Derivative,
and Signal Analysis  
  Peak Fitter 
Matlab File Exchange
"Pick of the Week"
 Interactive Power Spectrum Demo 
  Interactive Peak Fitter   

Python: a free and fast alternative

Areas of application where these programs are being applied  (PDF file)

Citations in published papers  (PDF file) 

Software used in this essay

Matlab, a high-performance commercial numerical computing environment and programming language that is widely used in research and education. For Windows, Macintosh, and Linux.  Lower-cost Home and Student versions available.


Octave, a freely downloadable alternative to Matlab, mostly compatible. For Windows, Macintosh, and Linux.


Python, a fast and free general purpose language for Windows, Unix, and Macintosh.

Click to enlarge    Click to

Microsoft Excel 2013                    OpenOffice Calc 4.1.1

Thanks to M. Farooq Wahab for his many contributions and for many fruitful discussions, to Baldassarre Cesarano for his close reading and typographical correction of this text, to Dr. Raphael Attie of NASA/Goddard Space Flight Center for corrections, to Diederick of The University of Hong Kong for code contributions, to Yuri Kalambet of Ampersand, Ltd., and to the many email correspondents who have made suggestions, asked questions, caught errors, and have shown me new types of data and new applications that have broadened the scope of this work.

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Copyright (c) 2021, Thomas C. O'Haver (toh@umd.edu)
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

First edition created in 1995. Last updated September, 2021. Created with SeaMonkey. This site is a retirement project and international community service, maintained by Prof. Tom O'Haver, Professor Emeritus, Department of Chemistry and Biochemistry, The University of Maryland at College Park, currently residing in Naples, FL. Comments, suggestions and questions should be directed to Prof. O'Haver at toh@umd.edu, currently residing in Naples, FL, and in Silver Spring, MD.

A Brief History of Mine

(Mining the literature using the Google Books Ngram Viewer)

Digital began to pull away from analog in the 1950s and now completely dominates.

In the mid 1990s, Web sites began to dominate earlier publishing technologies.

Transistors, invented in the late 1940s, pulled ahead of vacuum tunes in the 50s. By the early 80s, integrated circuits chips were dominant.

Statistics and quantitative signal and data processing have long been important, using computers after the 1950s.

"Derivative", "smoothing", and "convolution" are old concepts, but other signal processing terms don't become common until more recently.

The most common derivative orders have long been the first and second; higher older are much less used.

The Savitzky-Golay smooth is now the most often mentioned data smoothing technique. (What was going on the "triangular smooth" in the 1800s?)

The Gaussian profile is the most commonly encountered peak shape.

Measures of precision in the presence of random noise increased with the availability of electronic instrumentation.