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This page describes a series of downloadable Matlab
interactive signal processing tools for x,y time-series data.
Technical background, documentation, and examples of application
are provided in "A Pragmatic Introduction to Signal
Processing", available in HTML and
PDF formats.
The interactive functions listed on this page run
in the Figure window and use a simple set of keystroke commands,
rather than on-screen buttons or menus or sliders, in order to
reduce screen clutter, minimize overhead, and maximize
processing speed. Press K
to see the list of keystroke commands within each program. The
Figure window can be re-sized as you wish, including maximized
to full-screen to see the maximum detail in the signals, and can
be Saved in various formats, Copy/Pasted, or Printed, using the
standard Matlab menus. My goal is to make these programs very
easy to get working, with flexible input syntax, built-in help,
extensive online documentation, and many
simple examples that you can copy and paste into your Matlab
command window. Note:
all of the scripts and functions described below are written as
self-contained Matlab functions (m-files) and require no add-on
toolboxes to run. They have been developed and tested in Matlab
7.8 R2009a and in Matlab 8.1 R2013a.
For a complete list of my signal processing functions and
scripts, both interactive and command-driven, see functions.html. These scripts and
functions are downloaded about 1000 times per month on average and
have been used by thousands of scientists, engineers, researchers,
instructors, and students working in industry, environmental,
medical, engineering, earth science, space, military, financial,
agriculture, communications, and even music and linguistics. They
have been applied in many areas of
investigation and have been cited in over 145 published papers, theses, and
patents. Don't miss the amazing unsolicited
user comments below from actual users
of these programs. User comments and suggestions have often
resulted in changes and new features being added to the latest
versions; keep those emails coming.
First
time here? Check out these animated Web demos
of ipeak.m and ipf.m. Or download these Matlab
demo functions that compare ipeak.m with peakfit.m for
signals with a few peaks and signals with
many peaks and that shows how to adjust
ipeak to detect broad or narrow peaks.
These are self-contained demos that include all required Matlab
functions. Just place them in your path and click Run or type their name at the
command prompt. Or you can download all these demos together in idemos.zip. Note: Make sure you don't click on the
“Show Plot Tools” button in the toolbar above the figure;
that will disable normal program functioning. If you do;
close the Figure window and start again.
Author's appreciation: I
wish to express my thanks and appreciation for all those who have
made useful suggestions, corrected errors, and who have sent me
data from their work to test my programs on. These
contributions have really helped to correct bugs and to expand the
capabilities of my programs.
Matlab routines for locating and measuring the
peaks (or valleys) in noisy time-series data sets. It
detects peaks by looking for downward zero-crossings (or
upward zero-crossings
for valleys) in thesmoothed
first derivative then determines the position,
height, and width of each peak byleast-squares
curve-fitting of the raw data near the detected
peaks. (This is useful primarily for signals that have
several data points in each peak, not for spikes that
have only one or two points).
There are both command-line and interactive versions:
(1) a set of command-line functions for Matlab and Octave,
for finding peaks in signals and measuring their
positions, heights, widths, and areas by least-squares
curve-fitting, especially useful as modules to use in
your own custom scripts and functions to automate data
processing.
These tools are the ones to use when (a) the quantities of
greatest interest are the peak positions and amplitudes of
the positive peaks in your signal, (b) the peaks have
distinct (even if noisy) maxima, and (c) when you want all
the peaks numbered and quantified in one operation. You
can use the interactive iPeak function to
determine the ideal input arguments for the findpeaks.m and findpeaksfit.m
command-line functions. Note: the
latest version of iPeak can perform iterative
non-linear curve fitting on the peaks that it finds, using
the built-in peakfit.m
function (described below); this is useful for highly
overlapped or non-Gaussian peaks. For some demos,
download idemos.zip.
Using
simple keystrokes, you can adjust the signal
processing parameters continuously while observing
the effect on your signal dynamically. Click
here to download the ZIP file "iSignal5.zip"that
also includes some sample data for testing. You
can also download it from theMatlab File Exchange.
This is the tool to use when you want to explore and
clean up your signals and to try smoothing,
differentiation, and peak sharpening. It measures
things like peak-to-peak signal amplitude, standard
deviation, frequency spectra, and the area under the curve
of selected portions of your signal. It's also good for
quickly measuring
peak positions, heights, areas (one peak at a time)
and for determining how smoothing, differentiation, and
peak sharpening effect the signal and its frequency
spectrum. It can also pre-process signals to re-sample
them by interpolation, and reduce or remove artifacts such
as spikes (with the median filter) and steps (with a
rate-limiting filter).
Peak fitting programs for time-series
signals, which use anon-linear
optimization algorithmto decompose
a complex overlapping-peak signal into its component
parts. The objective is to determine whether your signal
can be represented as the sum of fundamental underlying
peaks shapes. Accepts signals of any length, including
those with non-integer and non-uniform x-values. Fits
groups of peaks of many different shapes).
There two different
versions:
(2) Interactive Peak Fitter, ipf.m, akeypress-operated interactive
version, for Matlab,
that allows you to pan and zoom through the signal to
pick the groups of peaks to fit.. Does
not work in Octave. There is an animated demonstration.
Using ipf.m
in Matlab, you can press a single keystroke to
instantly adjust the data range, change the peak shape,
number of peaks, baseline mode, or to re-calculate the fit
with different start or with a bootstrap subset of the
data. Super quick and easy.
The difference between them is that peakfit.m
is completely controlled by command-line input arguments and
returns its information via command-line output arguments; ipf.m
allows interactive control via keypress commands. Otherwise
they have the same curve-fitting capabilities. You
can also download a ZIP file
containing peakfit.m, DemoPeakFit.m,
ipf.m, Demoipf.m, some sample data for
testing, and a test script (testpeakfit.m)
that runs all the
examples sequentially to test for proper
operation.
These tools are the ones to use when (a) you need to measure
the peak positions, amplitudes, widths, and areas of the
positive peaks in your signal, (b) the peaks are highly
overlapped, (c) you want specific peaks in your signal
quantified, and (d) your peaks are approximately Gaussian,
Lorentzian, Pearson, Logistic, or exponentially-
broadened Gaussian. You can use the interactive ifp.m function to
determine the ideal input arguments for the peakfit.m and
command-line function. Note: iterative non-linear curve
fitting can also performed by the latest version of the
interactive peak finder
described above (iPeak). For some demos comparing peakfit.m
to iPeak.m, download idemos.zip.
iFilter is a Matlab implementation of aFourier
filterfunction
for time-series signals, including interactive versions
that allow you to adjust the filter parameters
continuously while observing the effect on your signal
dynamically. By adjusting the parameters, you can createlowpass,highpass, bandpass, andband-reject (notch), comb
pass, and comb reject filters with variable,
frequency, width, and cut-off rate. . The x-axis is
labeled for time-based signals, where the independent
variable is time in seconds, but the program can be used
with any frequency axis (e.g. spacial frequency, etc).Click here to view or download iFilter.m
You can also download it from theMatlab File Exchange.
Version 4.1, December, 2014.
This is the tool to use when you want to explore the
frequency components of your signals and to design a custom
filter that will optimize your signals.
Matlab implementation of a
computational method for quantitative analysis by
multiwavelength absorption spectroscopy, called the
transmission-fitting or “TFit” method, based on measuring
the underlying absorbance byfitting a modelof the
instrumentally-broadened transmission spectrum to the
observed transmission data, rather than by direct
calculation of absorbance as simply log10(Izero/I).
Advantages of the TFit method compared to conventional
methods are: (a) wider dynamic range; (b) greatly
improvedcalibration linearity;
(c) ability to operate under conditions that are
optimized forsignal-to-noise
ratioratio
rather than for optical ideality. With a linear
response, absorbance can be converted to concentration
simply by multiplying by a constant factor.
Just like themultilinear regression
(classical least squares)methods
conventionally used in absorption spectroscopy, the Tfit
method (a) requires an accurate reference spectrum of
each analyte, (b) utilizes multiwavelength data such as
would be acquired on diode-array, Fourier transform, or
automated scanning spectrometers, and (c) applies both
to single-component andmulti-component mixtureanalysis.
tfit.m
is a command-line demo function for Matlab or
Octave. TFitDemo.m
is an interactive demo m-file that works in recent
versions of Matlab. Version 2.1, November 2011.
Matlab keyboard-controlled interactive power spectrum
demonstrator, useful for teaching and learning about the
power spectra of different types of signals and the effect
of signal duration and sampling rate. Single keystrokes
allow you to select the type of signal (12 different preset
signals included), the total duration of the signal, the
sampling rate, and the global variables f1 and f2 which are
used in different ways in the different signals. If you know
some basic Matlab programming, you can even add your own
custom signal functions to this program. When the Enter
key is pressed, the signal (y) is sent to the Windows
WAVE audio device. Press K to see a list of all the keyboard
commands. Tested in Matlab version 7.8 (R2009a).
Click here to view or
download. You can also download it from the Matlab
File
Exchange. Version 2, October 2011
A set of
keyboard-controlled interactive demonstration modules,
written as self-contained Matlab functions, that are useful
for learning and teaching the
principles ofdiffraction
gratings. Shows a working cross
section
of the geometry of a diffraction grating (a common
illustration in textbooks of optics, spectroscopy, and
analytical chemistry). Single keystrokes allow you to
control such variables as the angle of incidence, grating
ruling density, wavelength, and diffraction order. One module
shows how the operation of a
diffraction grating emerges naturally just by adding up a
bunch of sine waves, without any higher math at all.
Press K to see a
list of all the keyboard commands. Tested in Matlab version
7.8 (R2009a).
Click here
to download ZIP file. You can also download it from
the Matlab
File
Exchange. Version 2, November 2011.
Notes
concerning the interactive functions ipeak.m, isignal.m,
and ipf.m:
(a)
Make sure you don't click on the “Show Plot Tools” button
in the toolbar above the figure; that will disable normal program
functioning. If you do; close the Figure window and start again.
(b) To facilitate transfer of settings from one of these functions
to another or to a command-line version,all these functions use
the W key to print out the syntax of other related functions, with
the pan and zoom settings and other numerical input arguments
specified, ready for you to Copy, Paste and edit into your own
scripts or back into the command window. For example, you can
convert an curve fit from ipf.m into the command-line peakfit.m
function; or you can convert a peak finding operation from ipeak.m
into the command-line findpeaksG.m or findpeaksb.m
or findpeaksb3.m functions.
(c) Recent versions of these three programs use the Shift-Ctrl-S,
Shift-Ctrl-F, and Shift-Ctrl-P keys to transfer the
current signal between iSignal.m, ipf.m, and iPeak.m
Background information on these and other signal processing
methods is available in:
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Copyright (c) 2014, 2016 Thomas C. O'Haver
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, sub-license, 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.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.