overshoot

Overshoot metrics of bilevel waveform transitions

Syntax

os = overshoot(x)

os = overshoot(x,fs)

os = overshoot(x,t)

[os,oslev,osinst] = overshoot(___)

[___] = overshoot(___,Name,Value)

overshoot(___)

Description

os = overshoot(x) returns overshoots expressed as a percentage of the difference between the low- and high-state levels in the input bilevel waveform. The values in os correspond to the greatest absolute deviations that are greater than the final state levels of each transition.

os = overshoot(x,fs) specifies the sample rate fs in hertz.

os = overshoot(x,t) specifies the sample instants t.

[os,oslev,osinst] = overshoot(___) returns the levels oslev and sample instants osinst of the overshoots for each transition. You can specify an input combination from any of the previous syntaxes.

[___] = overshoot(___,Name,Value) specifies additional options using one or more Name,Value arguments. You can use any of the output combinations from previous syntaxes.

overshoot(___) plots the bilevel waveform and marks the location of the overshoot of each transition. The function also plots the lower and upper reference-level instants and associated reference levels and the state levels and associated lower- and upper-state boundaries.

Examples

Overshoot Percentage in Posttransition Aberration Region

Determine the maximum percent overshoot relative to the high-state level in a 2.3 V clock waveform.

Load the 2.3 V clock data. Determine the maximum percent overshoot of the transition. Determine also the level and sample instant of the overshoot. In this example, the maximum overshoot in the posttransition region occurs near index 22.

load('transitionex.mat','x')

[oo,lv,nst] = overshoot(x)

oo = 
6.1798

lv = 
2.4276

nst = 
22

Plot the waveform. Annotate the overshoot and the corresponding sample instant.

overshoot(x);

ax = gca;
ax.XTick = sort([ax.XTick nst]);

Overshoot Percentage, Levels, and Time Instant in Posttransition Aberration Region

Determine the maximum percent overshoot relative to the high-state level, the level of the overshoot, and the sample instant in a 2.3 V clock waveform.

Load the 2.3 V clock data with sampling instants. The clock data are sampled at 4 MHz.

load('transitionex.mat','x','t')

Determine the maximum percent overshoot, the level of the overshoot in volts, and the time instant where the maximum overshoot occurs. Plot the result.

[os,oslev,osinst] = overshoot(x,t)

os = 
6.1798

oslev = 
2.4276

osinst = 
5.2500e-06

overshoot(x,t);

Overshoot Percentage, Levels, and Time Instant in Pretransition Aberration Region

Determine the maximum percent overshoot relative to the low-state level, the level of the overshoot, and the sample instant in a 2.3 V clock waveform. Specify the 'Region' as 'Preshoot' to output pretransition metrics.

Load the 2.3 V clock data with sampling instants. The clock data are sampled at 4 MHz.

load('transitionex.mat','x','t')

Determine the maximum percent overshoot, the level of the overshoot in volts, and the sampling instant where the maximum overshoot occurs. Plot the result.

[os,oslev,osinst] = overshoot(x,t,'Region','Preshoot')

os = 
4.8050

oslev = 
0.1020

osinst = 
4.7500e-06

overshoot(x,t,'Region','Preshoot');

Input Arguments

x — Bilevel waveform

real-valued vector

Bilevel waveform, specified as a real-valued vector. The sample instants in x correspond to the vector indices. The first sample instant in x corresponds to t = 0.

fs — Sample rate

real positive scalar

Sample rate in hertz, specified as a real positive scalar. The sample rate determines the sample instants corresponding to the elements in x.

t — Sample instants

vector

Sample instants, specified as a vector. The length of t must equal the length of the input bilevel waveform x.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'Region','Preshoot' specifies the pretransition aberration region.

PercentReferenceLevels — Reference levels

[10 90] (default) | 1-by-2 real-valued vector

Reference levels as a percentage of the waveform amplitude, specified as a 1-by-2 real-valued vector. The function defines the lower-state level to be 0 percent and the upper-state level to be 100 percent. The first element corresponds to the lower percent reference level, and the second element corresponds to the upper percent reference level.

Region — Aberration region

'Postshoot' (default) | 'Preshoot'

Aberration region over which to compute the overshoot, specified as 'Preshoot' or 'Postshoot'. If you specify 'Preshoot', the function defines the end of the pretransition aberration region as the last instant when the signal exits the first state. If you specify 'Postshoot', the function defines the start of the posttransition aberration region as the instant when the signal enters the second state. By default, the function computes overshoots for posttransition aberration regions.

SeekFactor — Aberration region duration

3 (default) | real-valued scalar

Aberration region duration, specified as a real-valued scalar. The function computes the overshoot over the specified duration for each transition as a multiple of the corresponding transition duration. If the edge of the waveform is reached or a complete intervening transition is detected before the aberration region duration elapses, the duration is truncated to the edge of the waveform or the start of the intervening transition.

StateLevels — Low- and high-state levels

1-by-2 real-valued vector

Low- and high-state levels, specified as a 1-by-2 real-valued vector. The first element corresponds to the low-state level and the second element corresponds to the high-state level of the input waveform.

Tolerance — Tolerance level

2 (default) | real-valued scalar

Tolerance level, specified as a real-valued scalar. The function expresses tolerance as a percentage of the difference between the upper and lower state levels. The initial and final levels of each transition must be within the respective state levels.

Output Arguments

os — Overshoots

vector

Overshoots expressed as a percentage of the state levels, returned as a vector. The length of OS corresponds to the number of transitions detected in the input signal. For more information, see Overshoot.

oslev — Overshoot level

column vector

Overshoot level, returned as a column vector.

osinst — Sample instants

column vector

Sample instants of pretransition or posttransition overshoots, returned as a column vector. If you specify fs or t, the overshoot instants are in seconds. If you do not specifyfs or t, the overshoot instants are the indices of the input vector.

More About

State-Level Estimation

To determine the transitions, the overshoot function estimates the state levels of the input bilevel waveform x by using a histogram method with these steps.

1. Determine the minimum and maximum amplitudes of the data.

2. For the specified number of histogram bins, determine the bin width, which is the ratio of the amplitude range to the number of bins.

3. Sort the data values into the histogram bins.

4. Identify the lowest and highest indexed histogram bins with nonzero counts.

5. Divide the histogram into two subhistograms.

6. Compute the state levels by determining the mode or mean of the upper and lower histograms.

The function identifies all intervals which cross the upper-state boundary of the low state and the lower-state boundary of the high state. The low-state and high-state boundaries are expressed as the state level plus or minus a multiple of the difference between the state levels.

Overshoot

The function computes the overshoot percentages based on the greatest deviation from the final state level in each transition.

For a positive-going (positive-polarity) pulse, the overshoot is given by

$$100\frac{(O-S_2)}{(S_2-S_1)}$$

where O is the maximum deviation greater than the high-state level, S₂ is the high state, and S₁ is the low state.

For a negative-going (negative-polarity) pulse, the overshoot is given by

$$100\frac{(O-S_1)}{(S_2-S_1)}$$

This figure shows the calculation of overshoot for a positive-going transition.

The red dashed lines indicate the estimated state levels. The double-sided black arrow depicts the difference between the high- and low-state levels. The solid black line indicates the difference between the overshoot value and the high-state level.

State-Level Tolerances

You can specify lower- and upper-state boundaries for each state level. Define the boundaries as the state level plus or minus a scalar multiple of the difference between the high state and the low state. To provide a useful tolerance region, specify the scalar as a small number such as 2/100 or 3/100. In general, the $$\alpha \%$$ region for the low state is defined as

$$S_1\pm \frac{\alpha }{100}(S_2-S_1),$$

where $$S_1$$ is the low-state level and $$S_2$$ is the high-state level. Replace the first term in the equation with $$S_2$$ to obtain the $$\alpha \%$$ tolerance region for the high state.

This figure shows lower and upper 5% state boundaries (tolerance regions) for a positive-polarity bi-level waveform. The thick dashed lines indicate the estimated state levels.

References

[1] IEEE Standard 181. IEEE^® Standard on Transitions, Pulses, and Related Waveforms (2003): 15–17.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2012a