Documentation |
Overshoot metrics of bilevel waveform transitions
OS = overshoot(X)
OS = overshoot(X,FS)
OS = overshoot(X,T)
[OS,OSLEV,OSINST]
= overshoot(...)
[...] = overshoot(...,Name,Value)
overshoot(...)
OS = overshoot(X) returns the greatest absolute deviations larger than the final state levels of each transition in the bilevel waveform, X. The overshoots, OS, are expressed as a percentage of the difference between the state levels. The length of OS corresponds to the number of transitions detected in the input signal. The sample instants in X correspond to the vector indices. To determine the transitions, overshoot estimates the state levels of the input waveform by a histogram method. overshoot 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. See State-Level Tolerances.
OS = overshoot(X,FS) specifies the sampling frequency in hertz. The sampling frequency determines the sample instants corresponding to the elements in X. The first sample instant in X corresponds to t=0.
OS = overshoot(X,T) specifies the sample instants, T, as a vector with the same number of elements as X.
[OS,OSLEV,OSINST] = overshoot(...) returns the levels, OSLEV, and sample instants,OSINST, of the overshoots for each transition.
[...] = overshoot(...,Name,Value) returns the greatest deviations larger than the final state level with additional options specified by one or more Name,Value pair arguments.
overshoot(...) plots the bilevel waveform and marks the location of the overshoot of each transition as well as the lower and upper reference-level instants and the associated reference levels. The state levels and associated lower and upper-state boundaries are also plotted.
X |
Bilevel waveform. X is a real-valued row or column vector. |
FS |
Sample rate in hertz. |
T |
Vector of sample instants. The length of T must equal the length of the bilevel waveform, X. |
OS |
Overshoots expressed as a percentage of the state levels. The overshoot percentages are computed based on the greatest deviation from the final state level in each transition. By default overshoots are computed for posttransition aberration regions. See Overshoot. |
OSLEV |
Level of the pretransition or posttransition overshoot. |
OSINST |
Sample instants of pretransition or posttransition overshoots. If you specify the sampling frequency or sampling instants, the overshoot instants are in seconds. If you do not specify the sampling frequency or sampling instants, the overshoot instants are the indices of the input vector. |
For a positive-going (positive-polarity) pulse, overshoot expressed as a percentage is
$$100\frac{(O-{S}_{2})}{({S}_{2}-{S}_{1})}$$
where O is the maximum deviation greater the high-state level, S_{2} is the high state, and S_{1} is the low state.
For a negative-going (negative-polarity) pulse, overshoot expressed as a percentage is
$$100\frac{(O-{S}_{1})}{({S}_{2}-{S}_{1})}$$
The following figure illustrates 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.
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
$${S}_{1}\pm {\scriptscriptstyle \frac{\alpha}{100}}({S}_{2}-{S}_{1})$$
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 α% tolerance region for the high state.
The following figure illustrates 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.
[1] IEEE^{®} Standard on Transitions, Pulses, and Related Waveforms, IEEE Standard 181, 2003, pp. 15–17.