Once created, an array (or its histogram) may be displayed from the PLOT MENU in several representations. The data may be presented as Smooth curves, Discrete segments, or as just the data Points without linkages. Data points are connected by straight line segments in "smooth" format; this mode is plotted more quickly and is suitable for large data arrays. "Discrete" format resembles a bar chart and is often appropriate for small arrays and histograms. Graphical connections are not made in "points" format. For large arrays (N > 1024) where multiple samples would be plotted in the same column, a straight line connecting the extreme values for that column is drawn. This allows the array to be plotted more quickly with little if any decrease in the information conveyed.
Several graphical displays are available: the data may be plotted as Real/Imaginary parts, as Magnitude/Phase, Power, or Log of the Power (displayed in dB). The Magnitude/Phase may be plotted in several ways, including with a range of the phase of 2 pi radians, of pi radians with bipolar amplitude, with unwrapped phase, or with the magnitude (or squared magnitude) of the real/imaginary parts computed and displayed independently for comparisons. The difference of the real and imaginary arrays may be displayed on one plot. Arrays may also be displayed as Argand Diagrams, i.e. a plot of the imaginary part vs. the real part of the complex value. Often called a "Lissajous" figure, this format is useful in a number of applications. To return to the PLOT MENU from any graphic display, just type <ESC>. When SIGNALS is run as a DOS application in Microsoft WINDOWS, any graphics screens generated in the PLOT MENU may be saved to the Clipboard by typing ALT-PR SCRN. These images then may be pasted into other applications, such as Adobe PhotoShop or Microsoft PowerPoint.
The sum, difference, product, ratio, and table lookup of the arrays may be viewed from the PLOT menu. However, it is important to note that these combinations are calculated for display only; they are not stored in an array. To use a sum, difference, etc. of two arrays in a subsequent operation, the process must be performed in the ARITHMETIC menu.
The default range of the phase is [-pi, pi), but other options are available via the Q-option in the Plot Menu. The other ranges of the phase are unwrapped and in the interval [-pi/2, pi/2) with bipolar amplitude.
Perhaps the most useful display mode is the VALUES option [V], which combines a graphical display of the real/imaginary parts with a tabular display of the amplitude of a selected pixel in several forms. On a color VGA or EGA system, the real part of the array is plotted as a white solid line and the imaginary part in color (cyan); in CGA or monochrome graphics, the imaginary part is plotted as a dotted line. A pixel is selected by typing the index (x coordinate) followed by "CR", or by scrolling with the left and right cursor keys, which adds/subtracts a selectable increment from the index. The table lists the real and imaginary parts, magnitude and phase (computed in the interval -pi <= phase < +pi), and the power in both linear and log10 (dB) units. The value of the phase is displayed in degrees, in radians, and in units of - radians. The amplitude of the imaginary part also is listed in units of - for convenience in those occasions when the data array is stored as magnitude/phase.
The sample is specified both by index address (for the spatial representation) and by the corresponding spatial frequency in cycles (and radians) per pixel (for frequency representations). The pixel increment (delta_x) is changed by successive factors of two via the up and down cursor, or by typing "I" followed by the desired increment. The array ordinates are circularly periodic, i.e. the ordinate is calculated modulo N.
A segment of the VALUES display may be enlarged via the "Zoom" option. To use, locate the cursor at the center pixel desired and type "z", an integer m (power of two), and "<ENTER>". The display is replotted with fewer pixels (N/m) centered on the cursor. Once zoomed, typing "z" plus <ENTER> replots the original Values display, while typing <ESC> returns to the PLOT MENU. The "%" option computes the statistics of data points within the windowed segment of the array.
The histogram and/or statistics arrays in REAL/IMAGINARY format may
be computed from the PLOT or OPERATIONS menu (# for histogram,
% for statistics). The histogram may be plotted on the screen, its
values examined, or a spreadsheet-format file created. Sample statistics
(mean, variance, and standard deviation) may be computed after the histogram
or independently. The statistics may be computed for an array displayed
with the VALUES option; if "zoomed" to display only a portion
of the array, the statistics are computed for the displayed samples only.
This allows measurement of subsections of interest, if desired. If the
histogram is computed first, the statistics include the entropy
of each array (i.e. quantity of information) for the selected number
If you have any questions or problems, if you would like to obtain the source code, or if you have any comments about how to make the program more useful/easier to use, please contact me at the above addresses/phone number. If you have access to the Internet, e-mail is the best way to reach me ("firstname.lastname@example.org").
RETURN to OVERVIEW of SIGNALS MANUAL
OPTIONS in MAIN MENU
OPTIONS in FUNCTIONS MENU (suggest that "Image Autoload" be turned off!)
OPTIONS in OPERATIONS MENU (suggest that "Image Autoload" be turned off!)
OPTIONS in ARITHMETIC MENU