WOLFRAM

HolderModel
HolderModel

New in 14

represents the single-input, single-output model of a zero-order hold.

HolderModel[specs]

represents a holder with specifications specs.

Details

  • HolderModel is known as zero-order hold (ZOH), first-order hold (FOH) and inverse sampling.
  • HolderModel is typically used to convert a discrete-time signal coming from a digital microcontroller or a digital signal processor to a continuous-time signal used when actuating in the physical world or with a model of the physical world.
  • A holder is the model of an operation that takes a discrete-time signal defined for integers and generates a continuous-time signal f(t)=g(TemplateBox[{{t, /, T}}, Floor]), where is the sampling period. This holds the value constant between samples.
  • The specification spec is an association and can have the following keys:
  • "InputVariables"{u[t]}input variables
    "Order"0hold order, a non-negative integer
    "OutputVariables"{y[t]}output variables
    "SamplingPeriod"1sampling period
    "SignalCount"1number of inputs and outputs
    "TemporalVariable"ttemporal variable
  • The "Order" property specifies the order of the extrapolation to use. An order extrapolator uses the previous points to derive an interpolating polynomial of degree . This polynomial is then used to extrapolate the value over the next sampling period.
  • HolderModel[]["prop"] can be used to obtain various properties of the model.
  • The value of "prop" can be any of the keys in spec and the following:
  • "Properties"list of property names
    "PropertyAssociation"property names and values as an association
    "PropertyDataset"property names and values as a dataset
    {p1,p2,}
  • values of properties pi

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

A zero-order hold (ZOH) model:

Out[1]=1

Its properties:

Out[2]=2

Simulate the response of a ZOH to a sinusoidal input:

Out[1]=1

Plot the response and the input sequence:

Out[2]=2

Scope  (9)Survey of the scope of standard use cases

A zero-order hold model:

Out[1]=1

A first-order hold:

Out[1]=1

A hold with custom properties:

Out[1]=1
Out[2]=2

List all available properties:

Out[1]=1

Obtain a specific property:

Out[1]=1

Obtain several properties:

Out[1]=1

Obtain the properties as an association:

Out[1]=1

As a dataset:

Out[1]=1

Simulate the response of a first-order hold to a sinusoidal sequence:

Plot the response and the sequence:

Out[2]=2

Decrease the sampling period to obtain a better approximation of the sinusoid:

Plot the response and the input sequence of the better approximation:

Out[4]=4

The lower sampling period results in a better approximation:

Out[5]=5

Applications  (1)Sample problems that can be solved with this function

A holder model is a subsystem of a sampled data system:

Simulate the system:

Out[2]=2

Plot the response:

Out[3]=3

Properties & Relations  (3)Properties of the function, and connections to other functions

A sampler model is essentially a time-based action:

The response based on WhenEvent:

Out[3]=3

The response of sampler model:

Out[4]=4

They are the same:

Out[5]=5

A first-order hold is based on a linear interpolation of the current and previous input values:

The variable is the current input value, is the previous input value and is the total time elapsed:

The discrete variables , and are updated at each sampling instant:

Out[3]=3

Solve for the slope and intercept of the linear interpolation:

Out[4]=4

The output expression:

Out[5]=5

Solve for the output signal:

Out[6]=6

The solution using the holder model:

Out[7]=7

They are the same:

Out[8]=8

A holder model inverses the operation of a sampler model:

A sampler model in series with a holder model:

Out[2]=2

The output signal is the same as the input signal:

Out[3]=3
Wolfram Research (2024), HolderModel, Wolfram Language function, https://reference.wolfram.com/language/ref/HolderModel.html.
Wolfram Research (2024), HolderModel, Wolfram Language function, https://reference.wolfram.com/language/ref/HolderModel.html.

Text

Wolfram Research (2024), HolderModel, Wolfram Language function, https://reference.wolfram.com/language/ref/HolderModel.html.

Wolfram Research (2024), HolderModel, Wolfram Language function, https://reference.wolfram.com/language/ref/HolderModel.html.

CMS

Wolfram Language. 2024. "HolderModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HolderModel.html.

Wolfram Language. 2024. "HolderModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HolderModel.html.

APA

Wolfram Language. (2024). HolderModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HolderModel.html

Wolfram Language. (2024). HolderModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HolderModel.html

BibTeX

@misc{reference.wolfram_2025_holdermodel, author="Wolfram Research", title="{HolderModel}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/HolderModel.html}", note=[Accessed: 24-May-2025 ]}

@misc{reference.wolfram_2025_holdermodel, author="Wolfram Research", title="{HolderModel}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/HolderModel.html}", note=[Accessed: 24-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_holdermodel, organization={Wolfram Research}, title={HolderModel}, year={2024}, url={https://reference.wolfram.com/language/ref/HolderModel.html}, note=[Accessed: 24-May-2025 ]}

@online{reference.wolfram_2025_holdermodel, organization={Wolfram Research}, title={HolderModel}, year={2024}, url={https://reference.wolfram.com/language/ref/HolderModel.html}, note=[Accessed: 24-May-2025 ]}