HolderModel
✖
HolderModel
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
open allclose allBasic Examples (2)Summary of the most common use cases
A zero-order hold (ZOH) model:

https://wolfram.com/xid/01zh10jo1o9-3gx57p


https://wolfram.com/xid/01zh10jo1o9-bw5lje

Simulate the response of a ZOH to a sinusoidal input:

https://wolfram.com/xid/01zh10jo1o9-t7t869

Plot the response and the input sequence:

https://wolfram.com/xid/01zh10jo1o9-7iqdiu

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

https://wolfram.com/xid/01zh10jo1o9-2t9lf0


https://wolfram.com/xid/01zh10jo1o9-5u5oou

A hold with custom properties:

https://wolfram.com/xid/01zh10jo1o9-u35dhe


https://wolfram.com/xid/01zh10jo1o9-672ced

List all available properties:

https://wolfram.com/xid/01zh10jo1o9-tzvb4x


https://wolfram.com/xid/01zh10jo1o9-37gfn7


https://wolfram.com/xid/01zh10jo1o9-wx4rkn

Obtain the properties as an association:

https://wolfram.com/xid/01zh10jo1o9-u87w8v


https://wolfram.com/xid/01zh10jo1o9-xvcaf7

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

https://wolfram.com/xid/01zh10jo1o9-oof61a

Plot the response and the sequence:

https://wolfram.com/xid/01zh10jo1o9-npm2n5

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

https://wolfram.com/xid/01zh10jo1o9-jnhtm6

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

https://wolfram.com/xid/01zh10jo1o9-d2z8az

The lower sampling period results in a better approximation:

https://wolfram.com/xid/01zh10jo1o9-ddcb76

Applications (1)Sample problems that can be solved with this function
Properties & Relations (3)Properties of the function, and connections to other functions
A sampler model is essentially a time-based action:

https://wolfram.com/xid/01zh10jo1o9-q8fmqf
The response based on WhenEvent:

https://wolfram.com/xid/01zh10jo1o9-kkfckl

The response of sampler model:

https://wolfram.com/xid/01zh10jo1o9-6qge3x


https://wolfram.com/xid/01zh10jo1o9-thnbcb

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

https://wolfram.com/xid/01zh10jo1o9-7754zx
The variable is the current input value,
is the previous input value and
is the total time elapsed:

https://wolfram.com/xid/01zh10jo1o9-ugqf79
The discrete variables ,
and
are updated at each sampling instant:

https://wolfram.com/xid/01zh10jo1o9-vu4m59

Solve for the slope and intercept
of the linear interpolation:

https://wolfram.com/xid/01zh10jo1o9-gtb6lj


https://wolfram.com/xid/01zh10jo1o9-sqhr5


https://wolfram.com/xid/01zh10jo1o9-q8alru

The solution using the holder model:

https://wolfram.com/xid/01zh10jo1o9-ne3tsv


https://wolfram.com/xid/01zh10jo1o9-0n00e2

A holder model inverses the operation of a sampler model:

https://wolfram.com/xid/01zh10jo1o9-2piv85
A sampler model in series with a holder model:

https://wolfram.com/xid/01zh10jo1o9-bqb6ba

The output signal is the same as the input signal:

https://wolfram.com/xid/01zh10jo1o9-ccrsii

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
]}
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
]}