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- __________________________________________________
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- ANALYSIS (v4.0)
- __________________________________________________
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- Copyright 1992, 1993 by Gene V. Wallenstein
- All rights reserved.
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- Last revision: 03/31/93
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- Software for Science and Engineering
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- Gene V. Wallenstein
- 5990 Pine Cone Court #406d1
- Lake Worth, Florida 33463 USA
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- CompuServe 75110,77
- Telephone (407) 750-3527
- Internet - Wallenstein@Walt.ccs.fau.edu
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- T A B L E O F C O N T E N T S
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- 1. Introduction
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- 2. Registration
- 2.1. What you get when you register
- 2.1.1 Upgrades - What's next?
- 2.1.2 User's Manual and Tutorial
- 2.1.3 Direct Support
- 2.2. Registration Form
- 2.3. Legal Stuff
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- 3. ANALYSIS Tools
- 3.1. Fast Fourier Transform (FFT)
- 3.2. Wavelet Analysis
- 3.3. Autocorrelation
- 3.4. Crosscorrelation
- 3.5. Coherence Analysis
- 3.6. Moments and the Distribution
- 3.7. Wigner-Ville Analysis
- 3.8. Digital Filtering
- 3.9. Graphics (2D and 3D)
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- 1. Introduction and System Requirements
-
- ANALYSIS is a time-series analysis package which includes a
- wide diversity of transformations and other techniques to
- locate and quantify patterns in a data set. Even though you
- may not be analyzing time-series data, ANALYSIS can still
- give the same kinds of information as might be extracted
- from time dependent events, however, the interpretation
- changes. The only requirement is that you simply have the
- data in ASCII single column format. Some types of analyses
- also require that you specify two data sets. You will easily
- know which modules require this by the directions on the
- first menu screen for each type of analysis. If you are
- required to import two data sets, you must concatenate them
- into a single file which is of course twice as long as each
- original file.
-
- There are two other general requirements to use this
- package.
-
- 1) The first is simply that you should have installed the
- ANSI.SYS in your CONFIG.SYS file. This was probably already
- done for you depending on your version of DOS, but just the
- same take a peak at the CONFIG.SYS file. This is a normal
- text file, so if you have to edit it be sure to save the
- file in text mode and avoid any special control characters
- that a word processor might put in it. Check to see if you
- have in your CONFIG.SYS file, a line which reads:
-
- DEVICE=ANSI.SYS
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- if you don't, edit the file and add this line to it. You can
- still run ANALYSIS without ANSI.SYS, but the cursor control
- used by this package is dependent on the ANSI standard and
- will probably behave a bit strange without it.
-
- 2) The second requirement is that your screen be at least
- 640 by 480. As with the ANSI.SYS requirement, ANALYSIS will
- still run on smaller screens, but some of the graphic
- displays may clip on screens much smaller than this. Give it
- a try.
-
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- 2. Registration
-
- ANALYSIS is distributed through a unique marketing concept
- called "shareware". The idea behind shareware is that you
- get the software and try it for a short grace period and if
- you intend to use it beyond that you register your copy with
- the author. The entire concept is based on an honor system
- among programmers and users, which has led to an outstanding
- base of high quality software without the high price usually
- associated with it. Also, shareware users are in the unique
- position of being able to contact the authors of the
- software they are using and get direct support in the form
- of manuals, phone help, and possible further customization
- of the software. Please read the list of added features you
- will receive when you become a registered user of ANALYSIS.
-
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- 2.1. What do I get when I register ANALYSIS?
-
- Most authors of shareware offer further features to
- registered users. Below is a list of the additional items
- provided to registered users of ANALYSIS.
-
- 2.1.1. Upgrades - What's next?
-
- Registered users of ANALYSIS pay a one time registration
- price and receive all upgrades free. The only cost is a
- minimal fee to cover the postage and handling of the disk.
- As a registered user you will receive notifications through
- the mail for updates of ANALYSIS.
-
- Several users have asked what is in store for new versions
- of ANALYSIS. Since in general we update ANALYSIS every 8-10
- months, I will simply provide a broad sketch of planned
- upgrades.
-
- Most users have commented that, above all, they would like
- to see more "number crunching" routines with as much
- flexibility as possible. In light of this, the following
- additions will be made to the next version(s) of ANALYSIS:
-
- 1) WAVELET - Additions to the wavelet module have already
- begun. These include a broader family of "mother wavelets",
- which can be viewed prior to use. We are also looking into
- algorithms for allowing the user to define their own "mother
- wavelet".
-
- 2) NON-LINEAR ANALYSIS - Several routines have already been
- written to estimate quantities such as the correlation
- dimension and Lyapunov exponents of an attractor. These are
- quantities used to characterize the geometry and dynamics of
- a system's attractor. They can thus be used to determine if
- a system is chaotic or not.
-
- 3) MODELING - Both linear and nonlinear modeling in the form
- of ordinary differential equations (ODEs). The idea here is
- to specify a general form of the ODEs and solve for the
- parameters by using optimality constraints on the fit and
- stability of the equations.
-
- 4) STATISTICAL TESTS - Some users have requested the
- inclusion of various statistical tests such as ANOVA and T-
- tests. We did not plan to incorporate much in the way of
- statistics beyond the first four moments and distribution,
- but considering the feedback obtained from our users, a
- general section for additional statistics will be added in
- the future.
-
- We encourage all our users to provide feedback about
- ANALYSIS along with any ideas they may have for future
- releases. This is the primary means by which we guide our
- updates.
-
- 2.1.2. User's Manual and Tutorial
-
- A laser-printed user's manual and tutorial which is actually
- and expanded version of section 3 of this file will be given
- to all registered users. This manual includes various
- examples of data analysis and explains which techniques are
- best in certain circumstances and the type of information
- which can be obtained from such methods. Several graphic
- examples are also used to assist the reader in the
- interpretation of the results obtained from using ANALYSIS,
- along with an extended list of references for future
- reading.
-
- 2.1.3. Direct Support
-
- All registered users of ANALYSIS will receive full support
- either over the telephone, internet, or via the regular
- mail, by using one of the contact points on the cover of
- this document. This information is also listed on the first
- information screen of the program as well. Typical support
- consists of addressing any problems which are encountered
- while running ANALYSIS on certain machines. NOTE: The
- leading cause of reported problems is simply not using the
- proper file format. Please refer to the screen accompanying
- the particular module you are using for any additional
- requirements on file format beside those already stated.
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- 2.2. ANALYSIS Registration Form
-
- There is a separate form in the file REGISTER.DOC, which is
- the registration form. To get a hardcopy of the file you can
- "copy" it to your printer by using C:>COPY REGISTER.DOC
- PRN. This command prints out the document assuming the
- REGISTER.DOC file is in the C:\ directory. You do not have
- to use this form, but try to include the following
- information when registering ANALYSIS:
-
- Name________________________________________________________
-
- Address_____________________________________________________
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- City/State/Zip______________________________________________
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- Disk Size 5.25_________ 3.5__________
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- Where did you find ANALYSIS?________________________________
-
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- The following fees apply to registration:
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- 1) Single user - $25.00
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- 2) Institution (under 10 machines) - $150.00
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- 3) Institution (over 10 machines) - $300.00
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- Send check or money order to:
-
- Gene V. Wallenstein
- 5990 Pine Cone Court #406d1
- Lake Worth, Florida 33463 USA
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- 2.3. Legal Stuff
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- 1) License - The user is granted the right (and encouraged)
- to copy this unregistered version and distribute it with no
- charge assuming it is unaltered . The user is also granted a
- grace period of 30 days in which to decide to register the
- software or not. During this grace period the software may
- be used free of charge.
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- 2) Copyright - ANALYSIS is protected under United States
- copyright law and international treaty provisions. Copyright
- 1993 by Gene V. Wallenstein; All rights reserved.
-
- 3) Reverse Engineering - Any form of reverse engineering
- such as reverse compiling or disassembly is strictly
- prohibited.
-
- 4) Disclaimer of Warranty - This software and manual are
- distributed "as is" and without warranties as to performance
- of merchantability or any other warranties whether expressed
- or implied. Because of the various hardware and software
- environments into which this program may be placed, no
- warranty of fitness for a particular purpose is offered.
- Good data processing procedure dictates that any program be
- thoroughly tested with non-critical data before relying on
- it. The user must assume the entire risk of using the
- program. Any liability of the seller will be limited
- exclusively to product replacement or refund of purchase
- price.
-
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- 3. ANALYSIS Tools
-
- The following is a brief description of the tools used by
- ANALYSIS. It is by no means exhaustive in its description
- but is merely intended to get the reader "up and running". A
- more detailed description of the techniques as well as a
- tutorial is provided to registered users (section 2.1.).
-
- 3.1. Fast Fourier Transform (FFT)
-
- The Fast Fourier Transform (FFT) is a technique used to
- locate regularities in a data set. It is a way of
- representing a very complicated data pattern in terms of its
- linear projection onto sinusoids of various frequency. Thus
- the data can be seen as the sum of many simple periodic
- patterns each with a specific frequency. The POWER SPECTRUM
- is a power by frequency graph (uses a Parzen window) which
- shows quantitatively how much of the original pattern is
- composed by each of the frequencies.
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- A second quantity which can be derived from the FFT is the
- phase angle. Since the original signal can be represented as
- a sum of periodic patterns, it may be important to know the
- temporal relationship among each of the simpler patterns.
- That is, if they are time-shifted with respect to one
- another or not. The PHASE SPECTRUM tells the user the phase
- angle at each frequency. Generally, the user is only
- interested in those frequencies containing relatively large
- amounts of the total power in the spectrum. Therefore,
- one may compare for instance the phase angle for numerous
- data sets at a specific frequency and its higher harmonics.
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- In general, the FFT is a good method to decompose a data set
- which has multiple frequencies embedded in it.
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- 3.2. Wavelet Analysis
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- Wavelet analysis is fairly new to mainstream signal
- processing. It is a projective technique similar to the FFT,
- however, rather than simply decomposing the signal into
- sinusoids of varying frequency, the data is represented as
- projections onto the affine group (translations and
- dilations). This means the data set can be represented as
- time translations of the mother wavelet (a basis function)
- and/or time dilations (i.e. shrinking or expanding the time
- scale of observation). ANALYSIS uses what is called the
- Mexican Hat as the mother wavelet (the function looks like a
- slice through a sombrero). The TRANSLATION SPECTRUM plots
- the relative magnitude of the original signal when projected
- onto the mother wavelet under various translations. The
- DILATION SPECTRUM is the same thing, only now the projection
- is onto dilations of the mother wavelet.
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- Typically, wavelet analysis is an excellent method for
- locating short-lived, high frequency patterns. This is
- because it avoids the time vs. frequency resolution problem
- inherent in Fourier analysis.
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- 3.3. Autocorrelation
-
- The autocorrelation function of a signal is a time dependent
- plot of the correlation of the signal with itself at
- different time lags. If the signal is periodic, the
- autocorrelation of the signal will also be. The initial
- value in the autocorrelation should be 1, since this is the
- first time point in the signal correlated with itself (zero
- time lag). Following this, a time lag of one point is
- introduced each time a correlation is computed until the
- final lag of (n-1) time points. The range of the
- autocorrelation signal is thus 1 to -1.
-
- Another use for the autocorrelation is to see where the
- signal loses all correlation with itself (i.e. Markov
- processes). This can be seen as the first zero crossing of
- the autocorrelation. Consequently, even a periodic signal
- will have a zero crossing in the autocorrelation function.
- By examing the autocorrelation function of a signal, one can
- tell when in time the signal is correlated with itself and
- to what degree.
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- 3.4. Crosscorrelation
-
- The crosscorrelation is similar to the autocorrelation
- function except it describes the correlation between two
- signals shifted in time. To use the crosscorrelation module
- in ANALYSIS, you must concatenate the two files into one in
- single column format. Thus the two original files must be of
- exactly the same number of points. This module is very
- useful for extracting information about the temporal
- dependency of one signal on another.
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- 3.5. Coherence Analysis
-
- Coherence is a frequency dependent measure which quantifies
- the magnitude of shared power between two signals. To use
- this module, the data must be in the same format as that
- used by the crosscorrelation analysis. Similar to the FFT,
- the POWER SPECTRUM is a magnitude by frequency graph, which
- in the case of coherence is normalized between 0 and 1. Thus
- if two signals have exactly the same amount of a given
- frequency in their composition, the coherence at that
- frequency will be 1. If they have little in common at a
- given frequency, the coherence magnitude is 0.
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- A second quantity of the coherence measure is the relative
- phase angle between the two signals at a given frequency.
- The measure of relative phase between two signals yields
- information about the synchrony of the signals at a specific
- frequency. The two signals may be in perfect synchrony (a
- relative phase of 0 degrees) or be exactly out of phase or
- perfect syncopation (180 degrees). This analysis provides a
- means of quantifying the relative degree of synchrony
- between any two signals at each of the frequencies of
- interest.
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- 3.6. Moments and the Distribution
-
- This module returns the first four moments of the data set
- (the mean, variance, skew, and kurtosis) and generates a
- graph showing its distribution. This information is of use
- when attempting to get a general feel for the data set and
- its characteristics. The information can also of course be
- used as a means to statistically quantify the data set in
- comparison with other data.
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- 3.7. Wigner-Ville Analysis
-
- The Wigner-Ville method of analysis is a technique which has
- similarities to both the FFT and Wavelet methods. It is a
- projection of a data signal onto a family of sinusoids as
- is the case of the FFT, however, it also depends on time
- translations of the signal. The Wigner-Ville method is
- particularly good at uncovering periodic patterns in data
- sets where the signal is not stationary (i.e. the data may
- have a strong trend). By using the Wigner-Ville analysis,
- the data signal can be decomposed into its frequency
- components which are of varying temporal duration.
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- When using the TRANSLATION SPECTRUM of this module, one must
- specify which frequency of interest to calculate the time
- dilation across, or if the interest is in the FREQUENCY
- SPECTRUM, the user must specify the time dilation to
- calculate across each frequency.
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- If you are dealing with a data set which has slow trends
- which shift the moments of the signal dramatically in time,
- the Wigner-Ville can be used as a check on the FFT
- calculation.
-
- 3.8. Digital Filtering
-
- The digital filtering module in ANALYSIS is a general
- purpose tool for filtering data sets at prescribed band
- widths. For example, if the user wishes to create a new data
- signal consisting of only the 8.0 to 12.0 Hz frequency
- components, one simply needs to specify the high-pass (8.0),
- the low-pass (12.0), and the sampling rate of the original
- data set. The resulting output can be viewed and sent to a
- file for further analysis. Digital filtering is often the
- best way to "clean up" a signal so that its true structure
- can be viewed more easily. This, for example, is often the
- case when the signal contains a large amount of higher
- frequency noise. The user wishing to get rid of this could
- simply use this module and set the high-pass to 0.0 Hz and
- the low-pass setting to whatever is sufficient to eliminate
- the "noise". However, caution must obviously be taken when
- deciding what does and does not constitute noise in a
- signal.
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- 3.9. Graphics (2D and 3D)
-
- The graphics routines in ANALYSIS will plot data in two and
- three dimensions. The 2D routine simply takes the single
- column of data and plots it with time as the X axis. The 3D
- routine takes the single column of data and breaks it down
- in such a way that the first three numbers represent the
- first point in 3 dimensional space, the next three the
- second point, and so on. For the 3D routine, the user is
- asked whether a connected plot or circles are desired to
- represent the data. Also, the user specifies the desired
- rotation in the polar and azimuthal directions. A polar
- rotation of 0 degrees would be looking directly down at the
- data from the north pole. A 90 degree polar rotation would
- place the line of view directly at the equator. A rotation
- in the azimuthal direction would be like a walk around the
- equator. Try an initial polar rotation of 65 degrees and an
- azimuthal rotation of about 35 degrees.
-