The interfacing of measurement instrumentation to small computers has now become standard practice in the modern science laboratory. Computers are used for data acquisition, data, and storage, using a large number of digital computer-based numerical methods. Techniques are available that can transform signals into more useful forms, detect and measure peaks, reduce noise, improve the resolution of overlapping peaks, compensate for instrumental artifacts, test hypotheses, optimize measurement strategies, diagnose measurement difficulties, and decompose complex signals into their component parts. These techniques can often make difficult measurements easier by extracting more information from the available data. Many of these techniques are based on laborious mathematical procedures and/or analog electronics that were not really practical before the advent of computerized instrumentation. It is important to appreciate the abilities,

This essay covers only basic topics
related to one-dimensional time-series signals, not
two-dimensional data such as images. It uses a pragmatic
approach and is limited to mathematics only up to the most
elementary aspects of calculus, statistics, and matrix math. I
use logical arguments, analogies, graphics, and animation to
explain ideas, rather than lots of formal mathematics. Data
processing without math? Not really! Math is *essential*,
just as it is for the technology of cell phones, GPS, digital
photography, the Web, and computer games. But you can get *started
*using these tools without understanding all the underlying
math and software details. Seeing it work makes it more likely
that you'll want to understand *how *it works. But in the
long run, it's not enough just to know how to operate the
software, any more than knowing how to use a word processor or a
MIDI sequencer makes you a good author or musician.

Why do I
title this document "*signal *processing" rather than "*data
*processing"? By "signal" I mean the continuous *x*,*y*
numerical data recorded by scientific instruments as time-series,
where *x* may be *time* or another quantity like *energy
*or *wavelength, *as in the various forms of
spectroscopy. "Data" is a more general term that includes *categorical
*data as well. In other words, I'm oriented to data
that you would plot in a spreadsheet using the *scatter*
chart type rather than *bar *or *pie *charts.

At the present time, this work does not cover image processing, pattern recognition, or factor analysis. For more advanced topics and for a more rigorous treatment of the underlying mathematics, refer to the extensive literature on signal processing and on statistics and chemometrics.

This site had its origin in one of the experiments in a course called "Electronics and Computer Interfacing for Chemists" that I developed and taught at the University of Maryland in the 80's and 90's. The first Web-based version went up in 1995. Subsequently it has been revised and greatly expanded based on feedback from users. It is still a work in progress and, as such, benefits from continued feedback from readers and users.

This tutorial makes considerable use of *Matlab*, a
high-performance commercial and proprietary numerical computing
environment and "fourth generation" programming language that is
widely used in research (14, 17, 19, 20), *Octave*, a free
Matlab alternative that runs almost all of the programs and
examples in this tutorial, and also Python,
a powerful but free and open-source language. There is a good
reason why Matlab is so massively popular in science and
engineering; it's powerful, fast, and relatively easy to learn.
A very important aspect of Matlab is the concept of functions,
which are self contained modules of code that accomplish a
specific task. Functions usually "take in" data, process it, and
"return" a result. (A trivial example is *a*=sqrt(*b*),
which takes the value of *b*, computes its square root,
and assigns it to the variable *a*). Once a function is
written, it can be used over and over and over again. Functions
can be "called" from the inside of other functions. Matlab comes
with built-in functions for doing data processing tasks like
matrix math, filtering, Fourier transforms, convolution and
deconvolution, multilinear regression, and optimization. *You
can write your own custom functions* to use in your future
programming projects, and you can download powerful toolboxes
and free user-contributed functions. Matlab can interface to C,
C++, Java, Fortran, and Python; and it's extensible to symbolic
computing and model-based
design for dynamic and embedded
systems.* There are many code examples in this text that
you can Copy and Paste (or drag and drop) into the
Matlab/Octave command line* to run or modify, which is
especially convenient if you can split your screen between the
two. *If you try to run one of my scripts
or functions and it gives you a "missing function" error, that
means either that you have not yet downloaded that item from
my web site or that you have not placed it in the "path". Look
for the missing item here,
download it into your path, and try again.* Type "help path" at the
Matlab/Octave command prompt for help and related commands.

Most of the
techniques covered in this work can also be performed in spreadsheets
(11, 22, 23) such as *Excel *or *OpenOffice Calc.
*

Octave (currently version 6.4.0)
and the OpenOffice
Calc (LibreOffice
Calc) spreadsheet program can be downloaded without cost
from their respective web sites. Python is also a
free download.

All of the
Matlab/Octave scripts and functions, and all of the spreadsheets
used here can all be downloaded from
this site at no cost; they have received extraordinarily
positive feedback from users. If you try to run one of my
scripts or functions and it gives you a "missing function"
error, look for the missing item on functions.html,
download it into your path, and try again.

If you are unfamiliar with Matlab, read these sections about basics and functions and scripts
for a quick start-up. Matlab is not really a general-purpose
programming languages like C++ or Python; rather, it is
specifically suited to numerical methods, matrix manipulation,
plotting of functions and data, implementation of algorithms,
creation of user interfaces, and deployment to portable devices
such as tablets - essentially the needs of numerical computing
by scientists and engineers. Matlab is more loosely
typed and less well structured in a formal sense than
other languages, and thus tends to be more favored by scientists
and engineers and less well liked by computer scientists and
professional programmers. To get a basic language like Python up
to the point where Matlab *starts *takes a considerable
effort and familiarity with computer jargon to install add-on
"packages" of functions that Matlab comes with. This is not a
criticism of Python, which is an extremely capable and
widley-used language, just an observation of different needs for
different fields.

There are
several versions of Matlab, including lower-cost student
and home
versions. See https://www.mathworks.com/pricing-licensing.html
for prices and restrictions in their use. It is possible
that your workplace may have a site license for Matlab. There
are also several other good free alternatives to MATLAB, in
particular Octave, which is essentially a Matlab clone, but
there is also Scilab, FreeMat, Julia,
and Sage
which are somewhat compatible with the MATLAB language and
which illustrate the influence of Matlab in the scientific
computing community. For a discussion of other possibilities,
see
http://www.dspguru.com/dsp/links/matlab-clones.

"People are generally better persuaded by the reasons which they have themselves discovered than by those which have come into the mind of others."

"A computer does not substitute for judgment any more than a pencil substitutes for literacy. But writing without a pencil is no particular advantage."

"

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