https://github.com/stdlib-js/simulate-iter-periodic-sinc
Create an iterator which generates a periodic sinc waveform.
https://github.com/stdlib-js/simulate-iter-periodic-sinc
cardinal diric dirichlet iterate iteration iterator javascript node node-js nodejs periodic processing signal simulate simulation sinc sine stdlib wave waveform
Last synced: 20 days ago
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Create an iterator which generates a periodic sinc waveform.
- Host: GitHub
- URL: https://github.com/stdlib-js/simulate-iter-periodic-sinc
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:09:20.000Z (almost 4 years ago)
- Default Branch: main
- Last Pushed: 2025-03-31T00:34:57.000Z (2 months ago)
- Last Synced: 2025-04-12T20:41:07.422Z (about 2 months ago)
- Topics: cardinal, diric, dirichlet, iterate, iteration, iterator, javascript, node, node-js, nodejs, periodic, processing, signal, simulate, simulation, sinc, sine, stdlib, wave, waveform
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 1.41 MB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
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# iterPeriodicSinc
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Create an iterator which generates a periodic [sinc][@stdlib/math/base/special/sinc] waveform.
The periodic [sinc][@stdlib/math/base/special/sinc] function, also known as the Dirichlet function, is defined as
```math
D_N(x; A) = \begin{cases}\frac{A\sin(Nx/2)} {N\sin(x/2)} & x \neq 2\pi k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \\ A (-1)^{k(N-1)} & x = 2\pi k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \end{cases}
```
where `N` is the function order and `A` is the peak amplitude. For odd `N`, the waveform has a period of `2π`, and, for even `N`, the waveform has a period of `4π`.
To express the periodic [sinc][@stdlib/math/base/special/sinc] function as a function of a discrete iteration number `t` and the waveform period `τ`, for odd `N`, let
```math
x = \frac{2\pi (t-\varphi)}{\tau}
```
and, for even `N`, let
```math
x = \frac{4\pi (t-\varphi)}{\tau}
```
where `τ` is the period (i.e., the number of iterations until a waveform repeats) and `φ` is the phase (iteration) offset. For odd `N`, we can thus substitute and express the periodic [sinc][@stdlib/math/base/special/sinc] function as
```math
D_N(t; A, \tau, \varphi) = \begin{cases}\frac{A\sin(N\pi(t-\varphi)/\tau)} {N\sin(\pi (t-\varphi)/\tau)} & t-\varphi \neq \tau k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \\ A (-1)^{k(N-1)} & t-\varphi = \tau k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \end{cases}
```
For even `N`, we can express the periodic [sinc][@stdlib/math/base/special/sinc] function similarly.
Note that the periodic [sinc][@stdlib/math/base/special/sinc] can be equivalently expressed as a function of the [sinc][@stdlib/math/base/special/sinc] function
```math
D_N(\pi x; N, A) = A \cdot \frac{\mathop{\mathrm{sinc}}(Nx/2)} {\mathop{\mathrm{sinc}}(x/2)}
```
## Installation
```bash
npm install @stdlib/simulate-iter-periodic-sinc
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var iterPeriodicSinc = require( '@stdlib/simulate-iter-periodic-sinc' );
```
#### iterPeriodicSinc( n\[, options] )
Returns an iterator which generates a periodic [sinc][@stdlib/math/base/special/sinc] waveform of order `n`.
```javascript
var it = iterPeriodicSinc( 7 );
// returns
var v = it.next().value;
// returns
v = it.next().value;
// returns
v = it.next().value;
// returns
// ...
```
The returned iterator protocol-compliant object has the following properties:
- **next**: function which returns an iterator protocol-compliant object containing the next iterated value (if one exists) assigned to a `value` property and a `done` property having a `boolean` value indicating whether the iterator is finished.
- **return**: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.
The function supports the following `options`:
- **period**: period (i.e., the number of iterations before a waveform repeats). Default: `100`.
- **amplitude**: peak amplitude. Default: `1.0`.
- **offset**: phase offset (in units of iterations; zero-based). A negative offset translates a waveform to the left. A positive offset translates a waveform to the right. Default: `0`.
- **iter**: number of iterations. Default: `1e308`.
By default, the function returns an iterator which generates a waveform that repeats every `100` iterations. To specify an alternative period, set the `period` option.
```javascript
var opts = {
'period': 1000
};
var it = iterPeriodicSinc( 7, opts );
// returns
var v = it.next().value;
// returns
v = it.next().value;
// returns
// ...
```
To adjust at what point the iterator begins in the waveform cycle, set the phase `offset` option. For example, to translate the waveform to the left,
```javascript
var opts = {
'period': 100,
'offset': -1
};
var it = iterPeriodicSinc( 7, opts );
// returns
var v = it.next().value;
// returns
v = it.next().value;
// returns
// ...
```
To translate the waveform to the right,
```javascript
var opts = {
'period': 100,
'offset': 1
};
var it = iterPeriodicSinc( 7, opts );
// returns
var v = it.next().value;
// returns
v = it.next().value;
// returns
// ...
```
By default, the function returns an infinite iterator (i.e., an iterator which never ends). To limit the number of iterations, set the `iter` option.
```javascript
var opts = {
'iter': 2
};
var it = iterPeriodicSinc( 7, opts );
// returns
var v = it.next().value;
// returns
v = it.next().value;
// returns
var bool = it.next().done;
// returns true
```
## Notes
- If an environment supports `Symbol.iterator`, the returned iterator is iterable.
## Examples
```javascript
var iterPeriodicSinc = require( '@stdlib/simulate-iter-periodic-sinc' );
// Create an iterator:
var opts = {
'period': 100,
'amplitude': 10.0,
'offset': -50,
'iter': 100
};
var it = iterPeriodicSinc( 7, opts );
// Perform manual iteration...
var v;
while ( true ) {
v = it.next();
if ( v.done ) {
break;
}
console.log( v.value );
}
```
* * *
## See Also
- [`@stdlib/simulate-iter/sine-wave`][@stdlib/simulate/iter/sine-wave]: create an iterator which generates a sine wave.
* * *
## Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
## License
See [LICENSE][stdlib-license].
## Copyright
Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].
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[npm-url]: https://npmjs.org/package/@stdlib/simulate-iter-periodic-sinc
[test-image]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/actions/workflows/test.yml?query=branch:main
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[coverage-url]: https://codecov.io/github/stdlib-js/simulate-iter-periodic-sinc?branch=main
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[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/tree/deno
[deno-readme]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/tree/umd
[umd-readme]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/tree/esm
[esm-readme]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/simulate-iter-periodic-sinc/main/LICENSE
[@stdlib/math/base/special/sinc]: https://github.com/stdlib-js/math-base-special-sinc
[@stdlib/simulate/iter/sine-wave]: https://github.com/stdlib-js/simulate-iter-sine-wave