# HolderModel

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 , 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" 0 hold order, a non-negative integer "OutputVariables" {y[t]} output variables "SamplingPeriod" 1 sampling period "SignalCount" 1 number of inputs and outputs "TemporalVariable" t temporal 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

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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.

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@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 ]}

#### BibLaTeX

@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 ]}