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A Pragmatic* Introduction to Signal Processing

 with applications in scientific measurement

An illustrated essay with free software and spreadsheet templates to download

This is a work in progress, last updated June 7, 2018. (Recently updated files)

A retirement project by Tom O'Haver , Professor Emeritus
Department of Chemistry and Biochemistry, University of Maryland at College Park

Have a question or suggestion? E-mail me: toh@umd.edu
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No cost, no
ads, no sign-in/registration, no eye candy, no frames, no hype, no Java, no Flash, no kidding. Completely free since 1993.

This essay is also available as a 153-page, indexed, printable document written in OpenOffice and saved in
Open Document** , Word   , and PDF formats. June 7
, 2018 version.  Readability index
A paperback printed version is available from Amazon CreateSpace in black-and-white ($11.00 US) and in color ($30.00 US).
This entire web site can be downloaded in archived HTML format complete with all linked software (183 MBytes).

Who uses this site?
   Amazing feedback from users
  Site search:

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

* Pragmatic: Relating to matters of fact or practical affairs, often to the exclusion of intellectual or artistic matters; practical as opposed to idealistic.
** What is Open Document format? See http://www.coolutils.com/Formats/ODT

 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 Measurement
 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  

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.


SPECTRUM, simple, freeware, 90s-era signal processing program, for Macintosh OS 8.

Click to enlarge    Click to

Microsoft Excel 2013                    OpenOffice Calc 4.1.1

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Copyright (c) 2018, 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 June, 2018. 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

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.