16 Histograms. Using Histograms to Reveal Distribution

Transcription

1 16 Histograms Using Histograms to Reveal Distribution The Histogram math function enhances understanding of the distribution of measured parameters (see the Disk Drive Analyzer Reference Manual for more detailed information on the workings of histograms). A histogram can identify the type of statistical distribution in the waveform, helping to establish whether signal behavior is expected or not. Distribution tails or extreme values related to noise, or other infrequent, non-repetitive sources, can also be observed. Also revealed by histograms are multiple frequencies or amplitudes that help in separating out jitter and noise. Histograms graph the statistical distribution of a parameter s set of values. The histogram bar chart is divided into intervals (bins). The height of each bar in the chart is proportional to the number of data points contained in each of its bins: the higher the bar, the more points there are in those bins and in the area of the waveform they represent. Before the DDA can generate histograms of the parameter values of input waveforms, the following must first be defined: The parameter to be made a histogram The trace on which the histogram will be displayed The maximum number of parameter measurement values to be used in creating the histogram The measurement range of the histogram The number of bins to be used These and the display of the histogram itself are done using the menus on the following pages. WP-DDA-UG-E Rev A ISSUED: October

2 Histograms Setting Up Histograms MATH TOOLS 1. Press to access the ZOOM + MATH menus. 2. Press the menu button corresponding to REDEFINE A, for example, which will place the histogram on Trace A. 3. Select Yes from the use Math? menu to enable math functions, including histograms. 4. Choose Histogram from the Math Type menu. Use Math? This is for activating the math functions. Math Type This is for selecting Histogram. MORE HIST SETUP Use this to access more histogram setup options and the final histogram dedicated menu (see next page). FIND CENTER AND WIDTH This is for positioning the histogram automatically when it has been calculated. It centers the histogram without affecting the zoom and position settings. Histogram custom line Use this to select the parameter to be made into a histogram, by means of the corresponding menu button or associated knob. You can select any of the configured parameters displayed on the line below the grid. using up to This is for selecting the number of values in the histogram, by means of the corresponding button or knob. A maximum of two billion values can be chosen for any one histogram ISSUED: October 2000 WP-DDA-UG-E Rev A

3 DDA HISTOGRAM Setting Binning and Scale Setup This allows you to adjust the histogram binning or scale settings. When Binning is selected, the classify into menu appears at the bottom of the menu panel. You can set the number of bins from 20 to 2000 in a sequence by pressing the corresponding menu button or turning the associated knob. For Scale options see next page. PARAMETER SETUP Use this to access the CHANGE PARAM menu group if you wish to select new parameters or modify the current settings. FIND CENTER AND WIDTH This is for calculating optimal center- and bin-width values for the histogram. classify into This is for choosing the number of bins into which the parameter events are to be classified, or distributed. Note: Each histogram is set by the user to display parameter values falling within a specified range. As the instrument captures the values in this range the bin counts increase. Values not falling within the range do not increment a bin in the histogram. To Display the Histogram: Press TRACE ON/OFF for the channel concerned. WP-DDA-UG-E Rev A ISSUED: October

4 Histograms HISTOGRAM Setting Binning and Scale Setup This allows you to adjust the histogram binning or scale settings. When Scale is selected, the menus shown here appear. vertical This is for setting the vertical scale: Linear sets a linear vertical scale. The baseline of the histogram designates a bin value of 0. As the bin counts increase beyond those that can be displayed on screen, the scale is automatically increased in a sequence. Log sets a logarithmic vertical scale. Because a value of 0 cannot be specified logarithmically, no baseline is provided. LinConstMax sets the vertical scaling to a linear value that uses close to the full vertical display capability of the instrument. The height of the histogram will remain nearly constant. The oscilloscope automatically increases the vertical scale setting as required, ensuring that the highest histogram bar does not exceed the vertical screen display limit. PARAMETER SETUP Use this to access the CHANGE PARAM menu group if you wish to select new parameters or modify the current settings. You can also use it to select Histogram Parameters (see next page). FIND CENTER AND WIDTH This is for calculating optimal center- and bin-width values for the histogram (see menus below it). Center Width Use this to set the histogram center value. Use this to set the histogram width value per division. The width per division multiplied by the number of horizontal display divisions (ten) determines the range of parameter values centered on the number in the Center menu that were used to create the histogram. NOTE: To Display the Histogram, press TRACE ON/OFF (for the channel) ISSUED: October 2000 WP-DDA-UG-E Rev A

5 DDA Applying Histogram Parameters You can apply additional histogram parameter values to measure particular attributes of the histogram itself (see the list on the next page). 1. Select PARAMETER SETUP to access the CHANGE PARAM menus. 2. Highlight Statistics in the Category menu and choose one or more histogram parameters from the measure menu to be placed using the On line menu. The CHANGE PARAM menus enable selection of Histogram Parameters such as sigma and range, and their placement on a line. In this figure, the histogram parameters sigma and range have been selected. Sigma determines the standard deviation of the histogram WP-DDA-UG-E Rev A ISSUED: October

6 Histograms distribution, while range gives the horizontal difference between the high and low values. The A beside the parameters listed under the grid indicates that the measurements are being made on Trace A the histogram. Also indicated: a sigma (A) value of 23.2 ps a range (A) value of 140 ps the icon indicates that these parameters are applied to a trace defined as a histogram. However, if these parameters were mistakenly set for a trace with no histogram, they would show ---. Zooms & Segments Clearing Events You can use the vertical and horizontal POSITION and ZOOM control knobs to expand and position the histogram, and to zoom on a particular feature. The resulting vertical and horizontal scale settings are shown in the displayed trace field for the trace. Histograms can also be displayed for traces that are zooms of segmented waveforms. When a segment from a zoomed trace is selected, the histogram for that segment will appear. Only the portion of the segment displayed, and which is between the parameter cursors, will be used in making the histogram. The displayed trace field will show the number of events captured for the segment. CLEAR SWEEPS Press at any time to clear histogram events. All events in the parameter buffer are cleared at the same time. However, the values in the Center and Width menus will not change, since they determine the range of the histogram and cannot be used to determine the parameter value range of a particular bin. If you reposition the histogram by means of the horizontal POSITION knob, the histogram s center will be moved from the center of the screen ISSUED: October 2000 WP-DDA-UG-E Rev A

7 DDA Histogram Parameter avg fwhm fwxx hampl hbase high hmedian hrms htop low maxp mode pctl pks range sigma totp xapk Definition average of data values in histogram full width (of largest peak) at half the maximum bin full width (of largest peak) at xx% the maximum bin histogram amplitude between two largest peaks histogram base or leftmost of two largest peaks highest data value in histogram median data value of histogram rms value of data in histogram histogram top or rightmost of two largest peaks lowest data value in histogram population of most populated bin in histogram data value of most populated bin in histogram data value in histogram for which specified x % of population is smaller number of peaks in histogram difference between highest and lowest data values standard deviation of the data values in histogram total population in histogram x-axis position of specified largest peak. WP-DDA-UG-E Rev A ISSUED: October

8 Histograms Using Cursors on Histograms Measurement cursors are useful for determining the value and population of particular histogram bins. MEASURE 1. Press to access the MEASURE group, and select Cursors from the top menu. 2. Choose the cursor required from the mode, type, and show menus (see Chapter 21 for more on cursors). The screen below shows the time cursor (downward pointing arrow) positioned on a selected bin in Trace A, which corresponds to the cross-hair cursor on the waveform. The value of the bin and its population are also indicated, in the Displayed Trace Label. Cursors enable measurement of particular histogram bins ISSUED: October 2000 WP-DDA-UG-E Rev A