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midcross

Mid-reference level crossing for bilevel waveform

Description

example

c = midcross(x) returns the time instants where each transition of the input signal x crosses the 50% reference level. To determine the transitions, the midcross function estimates the state levels of x by a histogram method and identifies all intervals which cross the upper-state boundary of the low state and the lower-state boundary of the high state.

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c = midcross(x,Fs) specifies the sample rate Fs.

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c = midcross(x,t) specifies the sample instants t.

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[c,midlev] = midcross(___) returns the waveform value corresponding to the mid-reference level. You can specify an input combination from any of the previous syntaxes.

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c = midcross(x,Name,Value) returns the time instants corresponding to mid-reference level crossings with additional options specified by one or more name-value arguments.

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midcross(___) plots the signal and marks the location of the mid-crossings (mid-reference level instants) and the associated reference levels. The function also plots the state levels with upper and lower state boundaries.

Examples

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Assuming a sampling interval of 1, compute the mid-reference level instant of a bilevel waveform. Plot the result.

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

midcross(x)

Figure Mid Cross Plot contains an axes object. The axes object with xlabel Time (seconds), ylabel Level (Volts) contains 9 objects of type line. One or more of the lines displays its values using only markers These objects represent signal, mid cross, upper boundary, upper state, lower boundary, mid reference, lower state.

ans = 21.5000

The instant at which the waveform crosses the 50% reference level is 21.5. This is not a sampling instant present in the input vector. midcross uses interpolation to identify the mid-reference level crossing.

Compute the mid-reference level instant for a sampled bilevel waveform. Use the time information to determine the sample rate, which is 4 MHz.

load('transitionex.mat','x','t')
Fs = 1/(t(2)-t(1))
Fs = 4000000

Use the sample rate to express the mid-reference level instant in seconds. Plot the waveform and annotate the result.

midcross(x,Fs)

Figure Mid Cross Plot contains an axes object. The axes object with xlabel Time (seconds), ylabel Level (Volts) contains 9 objects of type line. One or more of the lines displays its values using only markers These objects represent signal, mid cross, upper boundary, upper state, lower boundary, mid reference, lower state.

ans = 5.1250e-06

Compute the mid-reference level instant using a vector of sample times equal in length to the bilevel waveform. The sample rate is 4 MHz.

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

C = midcross(x,t)
C = 5.1250e-06

Annotate the result on a plot of the waveform.

midcross(x,t);

Figure Mid Cross Plot contains an axes object. The axes object with xlabel Time (seconds), ylabel Level (Volts) contains 9 objects of type line. One or more of the lines displays its values using only markers These objects represent signal, mid cross, upper boundary, upper state, lower boundary, mid reference, lower state.

Compute the level corresponding to the mid-reference level instant.

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

[~,midlev] = midcross(x,t)
midlev = 1.1388

Annotate the result on a plot of the waveform.

midcross(x,t);

Figure Mid Cross Plot contains an axes object. The axes object with xlabel Time (seconds), ylabel Level (Volts) contains 9 objects of type line. One or more of the lines displays its values using only markers These objects represent signal, mid cross, upper boundary, upper state, lower boundary, mid reference, lower state.

Obtain the 60% reference level instant and value for a bilevel waveform sampled at 4 MHz.

load("transitionex.mat","x","t")

[mc,Lev60] = midcross(x,t,MidPercentReferenceLevel=60)
mc = 5.1473e-06
Lev60 = 1.3682

Annotate the result on a plot of the waveform.

midcross(x,t,MidPercentReferenceLevel=60);

Figure Mid Cross Plot contains an axes object. The axes object with xlabel Time (seconds), ylabel Level (Volts) contains 9 objects of type line. One or more of the lines displays its values using only markers These objects represent signal, mid cross, upper boundary, upper state, lower boundary, mid reference, lower state.

Input Arguments

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Bilevel waveform, specified as a real-valued vector. The first sample instant corresponds to t=0.

Sample rate, specified as a positive real scalar in hertz.

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

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.

Example: c = midcross(x,t,MidPercentReferenceLevel=30)

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

Example: c = midcross(x,t,'MidPercentReferenceLevel',30)

Mid-reference level as a percentage of the waveform amplitude, specified as a scalar. For more information, see Mid-Reference Level.

Low- and high-state levels, specified as a 1-by-2 real-valued vector. The first element is the low-state level and the second element is the high-state level. If you do not specify 'StateLevels', the function estimates the state levels from the input waveform using the histogram method.

Tolerance levels (lower- and upper-state boundaries), specified as a scalar and expressed as a percentage. 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. For more information, see State-Level Tolerances.

Output Arguments

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Time instants of the mid-reference level crossings, returned as a vector.

Note

Because midcross uses interpolation to determine the crossing instant, c may contain values that do not correspond to sampling instants.

Mid-reference level, returned as a scalar.

More About

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Mid-Reference Level

The mid-reference level in a bilevel waveform with low-state level S1 and high–state level S2 is

S1+12(S2S1)

Mid Reference Level Instant

  • Let y50% denote the mid–reference level.

  • Let t50%- and t50%+ denote the two consecutive sampling instants corresponding to the waveform values nearest in value to y50%.

  • Let y50%- and y50%+ denote the waveform values at t50%- and t50%+.

The mid-reference level instant is

t50%=t50%+(t50%+t50%y50%+y50%)(y50%+y50%)

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

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

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 bilevel waveform. The thick dashed lines indicate the estimated state levels.

References

[1] IEEE® Standard on Transitions, Pulses, and Related Waveforms, IEEE Standard 181, 2003. p. 20.

Extended Capabilities

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

Version History

Introduced in R2012a