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


represents a holder with specifications specs.


  • 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
  • values of properties pi


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Basic Examples  (2)

A zero-order hold (ZOH) model:

Its properties:

Simulate the response of a ZOH to a sinusoidal input:

Plot the response and the input sequence:

Scope  (9)

A zero-order hold model:

A first-order hold:

A hold with custom properties:

List all available properties:

Obtain a specific property:

Obtain several properties:

Obtain the properties as an association:

As a dataset:

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

Plot the response and the sequence:

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

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

The lower sampling period results in a better approximation:

Applications  (1)

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

Simulate the system:

Plot the response:

Properties & Relations  (3)

A sampler model is essentially a time-based action:

The response based on WhenEvent:

The response of sampler model:

They are the same:

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:

Solve for the slope and intercept of the linear interpolation:

The output expression:

Solve for the output signal:

The solution using the holder model:

They are the same:

A holder model inverses the operation of a sampler model:

A sampler model in series with a holder model:

The output signal is the same as the input signal:

Wolfram Research (2023), HolderModel, Wolfram Language function, https://reference.wolfram.com/language/ref/HolderModel.html.


Wolfram Research (2023), HolderModel, Wolfram Language function, https://reference.wolfram.com/language/ref/HolderModel.html.


Wolfram Language. 2023. "HolderModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HolderModel.html.


Wolfram Language. (2023). HolderModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HolderModel.html


@misc{reference.wolfram_2024_holdermodel, author="Wolfram Research", title="{HolderModel}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/HolderModel.html}", note=[Accessed: 27-May-2024 ]}


@online{reference.wolfram_2024_holdermodel, organization={Wolfram Research}, title={HolderModel}, year={2023}, url={https://reference.wolfram.com/language/ref/HolderModel.html}, note=[Accessed: 27-May-2024 ]}