Antennas/Antennas_CD-ROM_Walnut_Creek_September_1996.iso/support/spectrum/sa.hlp

Text File | 1996-06-30 | 10KB | 322 lines

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                             INTRODUCTION

                                - SA -

                           Spectrum Analysis

SA is a program for the analysis of sequences in the time and frequency
domains.  All sequences are complex.  A limited capability to generate
sequences is provided.

SA's menus are hierarchical.  Commands may be issued by pressing the
highlighted letter or by moving to the desired command by <left arrow> or
<right arrow> and pressing <ENTER>.  The previous level menu may be selected
via selecting "Quit" or using the <ESC> key.  A <CR> will allow graceful exit
from unwanted prompts.  When a sequence is created or loaded from a file a
symbolic name is requested.  After operations are performed upon the sequence,
appropriate operation symbols are appended to the original name.  All symbolic
names are purely for information and all actions require reference to a
variable number.

Context sensitive help is available by pressing [F1] when there is not a
prompt.
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GENERATE

A limited capability is provided to generate real sequences.  The user is first
prompted for the number of data points desired in the sequence.  Next, the
following menu is presented:

              1:  k1·sin(k2·n+k3)    10:  k1·ε[n]+Σki·x[n-i]
              2:  k1·cos(k2·n+k3)    11:  Σki·ε[n-i]
              3:  k1·exp(k2·n)
              4:  k1·u(n-k2)
              5:  k1·ε[n], Normal(1σ,0µ)
              6:  k1·Uniform(1σ,0µ)
              7:  k1·n^k2
              8:  k1·k2^n
              9:  k1·δ(k2)

After the user selects the desired sequence term, he is prompted for the
proper constants.  After the constants are entered, the user is prompted as
to select whether this is a final term in the sequence or should this term
be added or multiplied by a following term yet to be specified.  An
unlimited number of terms may assembled in this manner to construct an
arbitrarily complex sequence.  Note that sequences created in this manner
are real.
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AUTOCORRELATION (Cxx)

The complex autocorrelation of the selected sequence is performed.  Note that
the resulting autocorrelation sequence will be twice as long as the original
sequence.
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CROSSCORRELATION (Cxy)

The complex crosscorrelation of the two selected sequences is performed.  Note
that the resulting crosscorrelation sequence will be twice as long as the
longer of the two original sequences.
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CONVOLVE

The complex convolution of two sequence is performed.
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INTEGRATION

The integration of the sequence is performed as a running sum whose initial
condition is zero.
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FILTER

The indicated sequence is filtered via a moving average.
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SUMMARY

Summary statistics (µ, σ, max, and min) are calculated for the indicated
sequence.
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FFT

The complex fast Fourier transform of the selected sequence is computed if
it is a power of two.  Otherwise, a warning is issued that the selected
sequence is not a power of two.  Since the FFT is appreciably faster than
the DFT, effort should be made to use power two sequences when possible.
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DFT

The complex discrete Fourier transform of the selected sequence is computed.
Since the DFT is appreciably slower than the FFT, the FFT should be selected
when possible.  The DFT is included for computation of non-power sequence
lengths.
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IDFT

The complex inverse discrete Fourier transform of the selected sequence is
computed.  Since the DFT is appreciably slower than the FFT, the FFT should
be selected when possible.  The DFT is included for computation of non-power
sequence lengths.
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IFFT

The complex inverse fast Fourier transform of the selected sequence is computed
if it is a power of two.  Otherwise, a warning is issued that the selected
sequence is not a power of two.  Since the IFFT is appreciably faster than
the DFT, effort should be made to use power two sequences when possible.
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RETRIEVE

After a variable name is assigned, the name of the file to be read is
requested.  The file extension "DAT" is assumed and need not be entered.
If another file extension is desired, it may be so entered.
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SAVE

After a variable # is assigned, the file name in which the data is to be saved
is requested.  The file extension "DAT" is assumed and need not be entered.
If another file extension is desired, it may be so entered.
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IMPORT

An ASCII "flat" file may be imported into a variable.  The imported file
format is assumed to be one number per line.  Each number is assigned to
a real or imaginary sequence point as determined by the response to the
prompt:
               Is the data to be real or imaginary (r/i) ? :
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ERASE

The indicated file is erased, the file extension "DAT" is assumed.
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DIRECTORY

A file directory of the currently logged drive and path is shown.  Only
files with the extension "DAT" are shown.
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PURGE

The sequence designated by the variable # is deleted.  This is useful in
reclaiming memory so that additional work may be performed.
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WINDOW

The data sequence may be window weighted by one of the following window
functions:

       a. Bartlett

             w[n] = 2n/(N-1),   0 ≤ n ≤ (N-1)/2
             w[n] = 2-2n/(N-1), (N-1)/2 ≤ n ≤ N-1

       b. Hamming

             w[n] = 0.54-0.46cos(2πn/(N-1)), 0 ≤ n ≤ N-1

       c. Blackman

             w[n] = 0.42-0.5cos(2πn/(N-1))+0.08cos(4πn/(N-1)), 0 ≤ n ≤ N-1

       d. Hanning

             w[n] = 0.5[1-cos(2πn/(N-1))], 0 ≤ n ≤ N-1
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UNARY

The following operators are provided which operate on one data sequence:

                         a.  Magnitude
                         b.  Magnitude Squared
                         c.  Complex Phase
                         d.  Complex Conjugate
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BINARY

The following operators are provided which operate on two data sequences:

                        a. Complex Addition
                        b. Complex Subtraction
                        c. Complex Multiplication

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CONSTANT

The following operators are provided which operate on one data sequence.

                a.  Add a complex constant to a sequence
                b.  Subtract a complex constant from a sequence
                c.  Multiply a sequence by a complex constant.
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REAL

The real part of the selected sequence is taken.

                    Re{x[n]} ═> y[n]
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IMAGINARY

The imaginary part of the selected sequence is taken.

                    Im{x[n]} ═> y[n]
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DATA

Files may be retrieved for manipulation by SA, or once data analysis has
been performed, the data may be saved for later use.  All data are saved in
ASCII format with a "DAT" extension automatically appended.  If another
file extension is desired, the complete file name may be specified when
saving a file.  When retrieving a file, the "DAT" extension is assumed and
need not be entered.  However, a file with any extension may be retrieved by
specifying the complete file name when prompted for the file name to retrieve.
File overwrite protection is provided.  All files with a "DAT" extension in the
current directory may be listed.

The "purge" command allows a sequence to be deleted from memory.  Purge does
not effect disk data.
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OPERATIONS

The following arithmetic operations may be performed on sequences:

    I.  Unary (One sequence involved in the operation):

           a.  Magnitude
           b.  Square Magnitude
           c.  Phase

    II.  Binary (Two sequences involved in the operation)

           a.  Addition
           b.  Subtraction
           c.  Multiplications

    III.  Constant (A sequence and a constant involved in the operation)

           a.  Addition
           b.  Subtraction
           c.  Multiplication


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FREQUENCY

This function provides the capability to perform frequency analysis.  A radix
two FFT which has a maximum capacity of 2048 complex data points is used.  A
DFT algorithm is provided for non-power two transforms.  If a non-power two
data sequence FFT is attempted, the user is notified so that a DFT algorithm
may be selected.  The following operations are available:

                     a. FFT (Fast Fourier Transform)
                     b. DFT (Discrete Fourier Transform)
                     c. IFFT (Inverse FFT)
                     d. IDFT (Inverse DFT)
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POWER
         a. Periodogram Power Spectrum Estimate (Magnitude squared of FFT)

         b. Bartlett Power Spectrum Estimate

            The Bartlett algorithm is an averaging periodigram.  The number
            of segments to be averaged must be a power of two.

         c. Welch Power Spectrum Estimate

            The Welch algorithm is an averaging periodigram.  The number
            of segments to be averaged must be a power of two.  Prior to
            computation of the periodigrams, each segment is multiplied by
            a Hanning window.

         d. dB

            10·log(x[n]) ═> y[n]
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TIME

The following time series analysis functions are provided:

                     a.  Cxx (Autocorrelation)
                     b.  Cxy (Crosscorrelation)
                     c.  Convolution
                     d.  Integration
                     e.  Moving average filter
                     f.  Summary Statistics
                         (1). Mean
                         (2). Standard Deviation
                         (3). Maximum and Minimum

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GRAPH

A limited graphing capability is provided.  All scaling is automatic.  The
graph display is exited by pressing any key.  A complex sequence may be
graphed as real and imaginary component amplitudes versus sample or imaginary
versus real.
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