The interfacing of measurement instrumentation to small computers
for the purpose of online data acquisition has now become standard
practice in the modern laboratory for the purposes of performing
signal processing and data analysis and storage, using a large
number of digital computer-based numerical methods that are used
to transform signals into more useful forms, detect and measure
peaks, reduce noise, improve the resolution of over-lapping 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, as
well as the limitations, of these techniques. But
in recent decades, computers and digital storage and processing
has become almost commonplace, much more accurate, far less
costly, easier to program, and literally millions of times
more capable altogether, reducing the cost of raw data and making
complex computer-based signal processing techniques both more
practical and necessary. It's not just the growth of
computers: there are now new materials, new instruments, new
fabrication techniques, new automation capabilities. We have
lasers, fiber optics, superconductors, supermagnets, holograms,
quantum technology, nanotechnology, and more. Sensors are now
smaller and cheaper and faster than ever before; we can measure over a wider range of
speeds, temperatures, pressures, and locations. There are new kinds of data
that we never had before. As Erik Brynjolfsson and
Andrew McAfee wrote in The Second Machine Age (W. W.
Norton, 2014): "...many types of raw data are getting dramatically
cheaper, and as data get cheaper, the bottleneck increasingly is
the ability to interpret and use data".
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. For
the math phobic, you should know that this essay does not dwell
on the math and that it contains more than twice as many figures
as equations. 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.
Some of the examples come from my
own areas of research in analytical chemistry, but these
techniques have been used in a wide
range of application areas. My software has been cited in
over 385
journal papers, theses, and patents, covering fields from
industrial, environmental, medical, engineering, earth science,
space, military, financial, agriculture, and even music and
linguistics. Suggestions and experimental data sent by hundreds of
readers from their own work has helped shape my writing and
software development. Much effort has gone into making this
document concise and understandable; it has been highly
praised by many readers.
At the present time, this work does not cover
image processing, wavelet transforms, 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), and Octave, a free
Matlab alternative that runs almost all of the programs and
examples in this tutorial. There is a good reason why this
language is so massively popular in science and engineering; it's
powerful, fast, and relatively easy to learn; it comes
with built-in functions for doing data processing tasks like
matrix math, Fourier transforms, convolution and deconvolution,
multilinear regression, and optimization; you can download
thousands of useful user-contributed functions; it 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.
Some of the illustrations were produced on my old
90s-era freeware signal-processing application for Macintosh
OS8, called S.P.E.C.T.R.U.M. (Signal
Processing for Experimental Chemistry Teaching
and Research / University of Maryland).
This is now an obsolete and retired version.
Most of the techniques covered in this work can
also be performed in spreadsheets
(11, 22, 23) such as Excel or OpenOffice Calc.
Octave
and the OpenOffice
Calc (LibreOffice
Calc) spreadsheet program can be downloaded without cost
from their respective web sites.
All of the Matlab/Octave scripts and functions,
the SPECTRUM program, 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 interfacing with programs
written in other languages - 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 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. There are also
several other good 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.
This work
is dedicated to the Joy of Uncompetitive Purposefulness.
"...in our culture of competitive self-comparison, we can
choose to amplify each other’s accomplishments because there
is, after all, enough to go around." Maria
Popova
"People are generally better persuaded by the reasons which they
have themselves discovered than by those which have come into
the mind of others." Blaise Pascal "...producing
technologies, and then teaching them to others, ... pushes
humankind ahead".David Premack
"A computer does not substitute for judgment any more than a
pencil substitutes for literacy. But writing without a pencil is
no particular advantage." Robert
McNamara
"...in the course of looking deeply within ourselves, we
may challenge notions that give comfort before the terrors of
the world. Supporters of superstition and pseudoscience are
human beings with real feelings, who, like the skeptics, are
trying to figure out how the world works and what our role in it
might be. Their motives are in many cases consonant with
science." Carl Sagan, in The
Demon-Haunted World: Science as a Candle in the Dark.
"...[be] full of wonder, generously open to every notion,
[dismiss] nothing except for good reason, but at the same time,
and as second nature, [demand] stringent standards of evidence,
...[applied] with at least as much rigor to what [you] hold dear
as to what [you] are tempted to reject with impunity."Carl
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30. “Numerical
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31. “Derivative Spectroscopy: Theoretical
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Updated June, 2019. This page is part
of "A
Pragmatic Introduction to Signal Processing", created
and maintained by Prof.
Tom O'Haver, Department of Chemistry and Biochemistry, The
University of Maryland at College Park. Comments, suggestions and
questions should be directed to Prof. O'Haver at toh@umd.edu.
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