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Complementary Cumulative Distribution Function: CCDF

Summary

CCDF computes the power complementary cumulative distribution (CCDF) function from a time domain signal. The CCDF curve shows the amount of time a signal spends above the average power level of the measured signal, or equivalently, the probability that the signal power will be above the average power level.

Parameters

Name Type Range
Block Diagram System Diagram N/A
Test Point System Meter N/A
Number of Bins Integer value >=2
Lower Threshold Real value <Upper Threshold
Upper Threshold Real value >Lower Threshold
Data Window in Samples Integer value >0
Sample Accumulation List of options N/A
Threshold Limit Handling List of options N/A
Y Axis Format List of options N/A
*Start Offset Real value >= 0
*Signal Delay List of options N/A

* indicates a secondary parameter

NOTE: If the selected system diagram is configured for a swept simulation, the measurement will have additional parameters for specifying the plotting configuration for each swept parameter. These parameters are dynamic and change based upon which data source is selected. See Section 1.3.3 in the AWR VSS Modeling Guide for details.

Result

This measurement returns real values.

Graph Type

This measurement can be displayed on a rectangular graph or tabular grid.

Computational Details

The CCDF curve is generated by first computing the probability density function (PDF) using a histogram of the measured signal. The number of samples histogrammed is determined by the Data Window in Samples and Sample Accumulation parameters. If Sample Accumulation is:

  • Only Data Window Samples: The number of samples is Data Window in Samples.

  • Cumulative: All the samples up to the current measured time are used (the current measured time is determined by the slider bar).

The samples are sorted by instantaneous power into Number of Bins bins. The thresholds of the bins are calculated from:

Pbin,min = LT+bin·(UT-LT)/N   bin=0,1,...,N-1

where Pbin,min is the smallest power value allowed in the bin, bin is the bin number, LT is the Lower Threshold parameter, UT is the Upper Threshold parameter, and N is the Number of Bins parameter.

Samples that fall below the Lower Threshold value or are greater than or equal to the Upper Threshold value are included in bin 0 and bin N-1, respectively, if Threshold Limit Handling is set to "Include all samples". If Threshold Limit Handling is set to "Exclude samples beyond threshold limits" these samples are not counted.

The PDF is then calculated for each bin by dividing the number of samples in the bin by the total number of samples counted. The cumulative distribution function (CDF), which is the integral of the PDF, is then calculated by:

The full CCDF is 1-CDF, which estimates the probability of a sample having an instantaneous power value greater than the maximum power in a given bin.

The CCDF measurement only displays the portion of the CCDF for power values greater than the average power of the histogrammed samples (any samples discarded because they are outside the threshold range are not included in the average power calculation.) The y-axis values displayed are the probabilities that a sample's instantaneous power will be greater than or equal to the power that is the x-axis value from the average power.

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