dsp.StateLevels
State-level estimation for bilevel rectangular waveform
Description
The dsp.StateLevels object estimates the state levels of
a bilevel rectangular waveform.
To estimate the state levels of a bilevel waveform:
Create the
dsp.StateLevelsobject and set its properties.Call the object with arguments, as if it were a function.
To learn more about how System objects work, see What Are System Objects?.
Creation
Description
sl = dsp.StateLevelssl, that estimates state levels in a bilevel
rectangular waveform using the histogram method with 100 bins.
sl = dsp.StateLevels(Name,Value)StateLevels
System object, sl, with each specified property set to the specified
value.
Properties
Usage
Description
Input Arguments
Output Arguments
Object Functions
To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named obj, use
this syntax:
release(obj)
Examples
State Levels of 2.3 V Underdamped Noisy Clock
Compute and plot the state levels of a 2.3 V underdamped noisy clock. Load the clock data in the variable, x, and the sampling instants in the variable t.
Note: If you are using R2016a or an earlier release, replace each call to the object with the equivalent step syntax. For example, obj(x) becomes step(obj,x).
load('clockex.mat','x','t');
Estimate the state levels.
sl = dsp.StateLevels; levels = sl(x);
Plot the clock data along with the estimated state levels and histograms.
plot(sl)
More About
State-Level Tolerances
Each state level can have associated lower- and upper-state boundaries. These state boundaries are defined as the state level plus or minus a scalar multiple of the difference between the high state and low state. To provide a useful tolerance region, the scalar is typically a small number such as 2/100 or 3/100. In general, the α% tolerance region for the low state is defined as
where S1 is the low-state level and S2 is the high-state level. Replace the first term in the equation with S2 to obtain the α% tolerance region for the high state.
This figure shows the lower and upper 2% state boundaries (tolerance regions) for a positive-polarity bilevel waveform. The estimated state levels are indicated by a dashed red line.
Algorithms
The dsp.StateLevels
System object uses the histogram method to estimate the states of a bilevel waveform. The
histogram method is described in [1]. To summarize the method:
Determine the maximum and minimum amplitudes and amplitude range of the data.
For the specified number of histogram bins, determine the bin width as the ratio of the amplitude range to the number of bins.
Sort the data values into the histogram bins.
Identify the lowest-indexed histogram bin, ilow, and highest-indexed histogram bin, ihigh, with nonzero counts.
Divide the histogram into two subhistograms. The lower-histogram bins are ilow ≤ i ≤ 1/2(ihigh — ilow).
The upper-histogram bins are ilow + 1/2(ihigh – ilow) ≤ i ≤ ihigh.
Compute the state levels by determining the mode or mean of the lower and upper histograms.
References
[1] IEEE® Standard on Transitions, Pulses, and Related Waveforms, IEEE Standard 181, 2003, pp. 15–17.