Software Vault: The Diamond Collection/The Diamond Collection (Software Vault)(Digital Impact).ISO/cdr05/freq21.zip/FRQ.TXT

Text File | 1995-03-11 | 12KB | 282 lines

    FREQ for Windows    ...Beyond Fourier Transforms...

    (c) 1995 CoDebris    All rights reserved     March 10, 1995
    711 Barbara Avenue  Solana Beach, CA 92075   [phone]

    This is the shareware (unregistered) version 2.1 of FREQ.  FREQ is
    a data analysis tool which determines what sine waves make up a
    data set or time series: periods, amplitudes, phases, percent
    relative power).  You specify which periods you believe are present
    (or specify a whole range of periods), and FREQ tests those periods
    and graphically assembles selected sine waves into a revealing
    portrait of your data: a visualization of your data you can't get
    from a Fast Fourier Transform without a whole lot of work and
    specialized training.

    The registered version of FREQ (ver 2.2) performs a host of related
    analysis and data synthesis functions: a "waveform spreadsheet".
    Registration is $40, cash or check, payable to CoDebris at the above
    address.  On registration we will either mail you a 3.5" floppy disk
    or send you e-mail with an attached FREQ.ZIP file containing the
    upgrade, and more tutorial data files with associated period tables.


Notice...

    We do not modify ANY of your system files, and de-installing FREQ
    is accomplished by simply deleting the FREQ Program Group and the
    files, which are usually found in C:\FREQ.


Overview...

    Researchers and analysts often want to know if experimental data
    (a time series) contains significant amounts of signal at
    frequencies of interest to them.  These frequencies may correspond
    to driving forces, environmental constraints (boundary conditions),
    or system responses, and may result from intrinsically non-linear
    processes.  Often, mathematical or phenomenological models exist to
    explain some observed behavior, and experimental data is collected
    to verify whether or not the model is correct.

    FREQ is a new, fundamentally unique tool for performing these
    analyses.  FREQ not only identifies the period, phase and amplitude
    of sine waves which represent your data, but then plots each new
    wave component over a graph of your data.  A plot of the original
    data and reconstruction can be printed, and the reconstruction can
    even be saved as a data set, on the same scale as the original data.



Installation and Operation...

    If you obtained FREQ from a download, run PKUNZIP FREQ.ZIP and then
    run SETUP to install FREQ in a Program Group under Windows 3.1.

    If you have FREQ on a 3 1/2" floppy disc, install FREQ by running
    SETUP from the floppy drive.

    During setup, you are prompted for a directory in which to install
    FREQ, the default is C:\FREQ.

    Extensive on-line help is accessible from the menu Help/Contents
    option.

    On first running FREQ, choose Analyze/Frequency Search from the
    menu and select a (supplied) table of candidate periods (use
    REAL.TBL the first time) and a supplied data file (REAL.DAT).
    The .TBL files can be edited and saved using FREQ's built-in
    editor.

    REAL.DAT is a physiological data set.  The synthesized curve is
    not a bad approximation to the data, as you can see while the
    reconstruction builds before your eyes, even though only 55% of
    the "power" is accounted for by the seven identified periods,
    amplitudes and phases, analyzed in under 1 minute.  Refining the
    REAL.TBL file might find even better (closer) periods to use,
    but the periods supplied are pretty good, or they wouldn't be used
    in a demo.

    The important thing is watching the highest-power, long period
    sines define major trends in the data and seeing the short-period
    sines fill in the peaks and valleys.  On seeing this for the first
    time, you can achieve a very intuitive sense for what the data
    says, and of Fourier series in general.

    As you feed FREQ other data sets of interest to you, or generated
    from the rich variety of Synthesis options in FREQ, your
    understanding of what your data is telling you grows immediately,
    in a very visual way.

    Arrange your data for input to FREQ by creating a file consisting
    of two columns (X, Y) and as many rows as there are points in the
    data set.  Alternatively, you can just feed FREQ a single column
    of Y values only, and tell FREQ the initial X value and the
    interval between successive values.

    FREQ will line-plot the actual data in green, and the synthesized
    data (the "reconstruction") from the selected periods as a yellow
    dotted line.  Plots are auto-rescaled on window resizing, actually
    recomputed every time the window is painted to optimize the
    displayed data information content.

    Each time a new period is selected as containing the next most
    significant amount of power, the yellow curve is redrawn to
    include the new information.  You can get a good sense for periods
    to include in the .TBL file, and which to exclude, by watching the
    analysis and then examining the .OUT file that pops up on the
    screen after each analysis is complete.

    In fact, watching the earlier, higher-power sinusoids define the
    major features of your data is an insightful experience; one
    researcher termed it a "spectacular visualization" of his data.
    The side slopes of the sine curve will lie along major trends in
    the data, and the peaks won't necessarily correspond to peaks in
    the data.  That is left to shorter period components, which when
    properly phased with the long period components will ride up and
    down peaks in the data with increasing fidelity.

    You will definitely learn to think nearly simultaneously in
    so-called "dual spaces": time and frequency.  You will learn to
    think carefully about what are the proper "units", or "dimensions"
    of your data.  The supplied PERIOD.TBL is designed to encompass a
    wide range of possible values, but it takes longer to analyze a
    data set.  After running it on your data, examine the associated
    .OUT file and create a "tailored" table of periods to run with
    that particular sort of data.  Use it to test assumptions about
    what is really in your data.



Background...

    The usual frequency analysis approach is to pre-process your data,
    apply a Fast Fourier Transform to the series, and plot the power
    spectrum.  Peaks in the FFT spectrum may correspond to interesting
    frequencies.  However, it is difficult for anyone but a signal
    processing expert to know how much power in the time series is
    actually accounted for by a given frequency.  It is even harder to
    resolve nearby, overlapping broad peaks.  More often than not,
    "noise" dominates the data and cannot easily be de-coupled from
    signals of interest.

    Pre-processing (filtering and windowing) of data sets is a very
    demanding discipline, and many of the rules to assure the validity
    of pre-processing operations are difficult to apply, as such
    operations actually modify the characteristics of the manipulated
    data.

    Further, most researchers with a need for waveform analyses do not
    have formal training in the subject, and many feel uncomfortable
    with having to use a host of implicit assumptions.

    There is an alternative, nearly painless method available to
    perform such frequency analyses.  The researcher first prepares
    (as a text file) a table of candidate periods.  On initial
    creation, the table usually contains a fairly large number of
    entries, as there may be no prior knowledge of what is really
    present in the data.  Periods may be longer than the time series,
    or as short as twice the time interval between points.  But the
    researcher often knows what to look for based on theory or
    existing work, and the table will contain several periods in the
    regions of interest.

    FREQ is not just a curve-fitter, nor is it simply an FFT.  To use
    it, you should know something about your data, but you need nearly
    no data analysis background.  FREQ searches your data using the
    supplied candidate periods in a .TBL file which you prepare,
    selecting those periods which account for the most "power".

    FREQ uses an adaptation, called Fast Orthogonal Search (FOS), of
    the Orthogonal Search Method developed by Michael J. Korenberg and
    his group at Queens University in the late 1980's.  The algorithm
    is applied to your data set, using an associated table of candidate
    periods.  The precise power, amplitude, and phase of sine waves
    corresponding to entries in the table is displayed.  The objective
    is to determine if frequencies of interest to the researcher are
    present in significant measure, and report the results.

    The algorithm analyzes a time series stepwise, determining the
    ability of each period to explain a significant portion of the
    total variance (mean square error, or MSE: roughly, the data
    set's "power").  It then orthogonally removes the sinusoid
    explaining the largest percentage of the time series variance.
    This process is repeated on the residuals until there is no further
    significant error reduction or until a specified number of periods
    have been identified.

    The algorithm is capable of much greater time resolution than a
    Fourier transform, and is not limited to harmonics of a fundamental
    frequency.  It is also quite insensitive to noise, as all data
    elements are used only in series-wide averages over the orthogonal
    basis functions.  Finally, it tolerates missing data points,
    irregularly-spaced data sets, and short data segments.  In many
    nonlinear or biological systems, the signal frequencies move, or
    breathe, as the system evolves, so short segments are necessary
    for system identification.

    FREQ is a Multiple Document Interface application, so it will
    display the results from multiple Frequency Searches on-screen at
    the same time, including the reconstructions (dotted yellow plots)
    and text output files.  A rudimentary FFT is included, mostly for
    contrast.



Registration and Upgrades...

    If you run FREQ and like it, let us know (register it).  If you
    run it and don't like something about it, let us know that too.
    FREQ is becoming a fairly comprehensive waveform analysis and
    synthesis package, and most features are added in response to
    user suggestions: in the works are digital filters, multi-variate
    data sets and non-linear dynamics tools.

    In addition to everything in the shareware version, the registered
    version of FREQ (ver. 2.2) contains these additional functions:

        Synthesize: Pre-Process Data Set...
                        Interpolate
                        Segment
                        Smooth
                        Remove Trend
                        Remove Artifacts
                        Subtract Mean
                        Scale X or Y Data
                        Offset X or Y Data
                        RMS Partition
                    Copy Current Data Set
                    Two-Graph Operations...
                        Concatenate (Join) Data Sets
                        Add Data Sets Pointwise
                        Subtract Data Sets
                        Multiply Data Sets
                        Divide (Ratio) Data Sets
                    Reconstruct Data Set From Search Sines

        Analyze:    Fast Fourier Transform
                    Inverse FFT
                    Approximate Entropy


        The next upgrade to FREQ (ver. 2.4) will add these features:

            Multi-variate data sets (e.g. simultaneous heart rate,
            EEG, cardiovascular output vs. time)

            Log/linear, linear/log, log/log graphs

            Windowing:  Hamming, Hann

            Filters:    Bessel, Butterworth, Chebychev, Elliptical
                        Ideal Low/High/Band Pass
                        Notch, Comb and Band Stop

            Convolution, Correlation analyses

            Non-linear analyses: Poincare plot, Second Return,
            Min Info, Lyapunov dimension

            Full-resolution (not scaled bitmap) printed graphs,
            color optional, with settable titles, legends, and
            captioning.

        Registrations received BEFORE July 1, 1995 can receive
        this version 2.4 upgrade deep-discounted during August.

        In July, the registration price will become $60.


    We are very interested in enlarging the variety of data set formats
    FREQ can recognize: let us know if you want FREQ to read your
    spreadsheet or data base files or accept data from acquisition
    hardware: sound boards, DSP boards, A/D or digital I/O boards.



    Gene Zawadzki
    CoDebris
    [phone]
    CompuServe 72074,772