npm package: @stdlib/simulate-iter-periodic-sinc
Description: Create an iterator which generates a periodic sinc waveform.
Author: The Stdlib Authors
Latest version: 0.2.3

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# iterPeriodicSinc

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Create an iterator which generates a periodic [sinc][@stdlib/math/base/special/sinc] waveform.

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

The periodic [sinc][@stdlib/math/base/special/sinc] function, also known as the Dirichlet function, is defined as

<!-- <equation class="equation" label="eq:periodic_sinc" align="center" raw="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}" alt="Periodic sinc function."> -->

<div class="equation" align="center" data-raw-text="D_N(x; A) = \begin{cases}\frac{A\sin(Nx/2)} {N\sin(x/2)} &amp; x \neq 2\pi k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots  \\ A (-1)^{k(N-1)} &amp; x = 2\pi k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \end{cases}" data-equation="eq:periodic_sinc">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d985bb501380970d8c79ffba20ce15965a7acfa9/lib/node_modules/@stdlib/simulate/iter/periodic-sinc/docs/img/equation_periodic_sinc.svg" alt="Periodic sinc function.">
    <br>
</div> -->

<!-- </equation> -->

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

<!-- <equation class="equation" label="eq:periodic_sinc_substitution_odd" align="center" raw="x = \frac{2\pi (t-\varphi)}{\tau}" alt="Periodic sinc function substitution for odd N."> -->

<!-- <div class="equation" align="center" data-raw-text="x = \frac{2\pi (t-\varphi)}{\tau}" data-equation="eq:periodic_sinc_substitution_odd">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d985bb501380970d8c79ffba20ce15965a7acfa9/lib/node_modules/@stdlib/simulate/iter/periodic-sinc/docs/img/equation_periodic_sinc_substitution_odd.svg" alt="Periodic sinc function substitution for odd N.">
    <br>
</div> -->

<!-- </equation> -->

and, for even `N`, let

<!-- <equation class="equation" label="eq:periodic_sinc_substitution_even" align="center" raw="x = \frac{4\pi (t-\varphi)}{\tau}" alt="Periodic sinc function substitution for even N."> -->

<!-- <div class="equation" align="center" data-raw-text="x = \frac{4\pi (t-\varphi)}{\tau}" data-equation="eq:periodic_sinc_substitution_even">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d985bb501380970d8c79ffba20ce15965a7acfa9/lib/node_modules/@stdlib/simulate/iter/periodic-sinc/docs/img/equation_periodic_sinc_substitution_even.svg" alt="Periodic sinc function substitution for even N.">
    <br>
</div> -->

<!-- </equation> -->

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

<!-- <equation class="equation" label="eq:periodic_sinc_in_terms_of_period" align="center" raw="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}" alt="Periodic sinc function as a function of the waveform period."> -->

<!-- <div class="equation" align="center" data-raw-text="D_N(t; A, \tau, \varphi) = \begin{cases}\frac{A\sin(N\pi(t-\varphi)/\tau)} {N\sin(\pi (t-\varphi)/\tau)} &amp; t-\varphi \neq \tau k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots  \\ A (-1)^{k(N-1)} &amp; t-\varphi = \tau k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \end{cases}" data-equation="eq:periodic_sinc_in_terms_of_period">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d985bb501380970d8c79ffba20ce15965a7acfa9/lib/node_modules/@stdlib/simulate/iter/periodic-sinc/docs/img/equation_periodic_sinc_in_terms_of_period.svg" alt="Periodic sinc function as a function of the waveform period.">
    <br>
</div> -->

<!-- </equation> -->

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

<!-- <equation class="equation" label="eq:periodic_sinc_in_terms_of_sinc_function" align="center" raw="D_N(\pi x; N, A) = A \cdot \frac{\operatorname{sinc}(Nx/2)} {\operatorname{sinc}(x/2)}" alt="Periodic sinc function in terms of the sinc function."> -->

<!-- <div class="equation" align="center" data-raw-text="D_N(\pi x; N, A) = A \cdot \frac{\operatorname{sinc}(Nx/2)} {\operatorname{sinc}(x/2)}" data-equation="eq:periodic_sinc_in_terms_of_sinc_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d985bb501380970d8c79ffba20ce15965a7acfa9/lib/node_modules/@stdlib/simulate/iter/periodic-sinc/docs/img/equation_periodic_sinc_in_terms_of_sinc_function.svg" alt="Periodic sinc function in terms of the sinc function.">
    <br>
</div>

<!-- </equation> -->

<!-- TODO: add a figure showing a periodic sinc waveform -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/simulate-iter-periodic-sinc
```

</section>

<section class="usage">

## 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 <Object>

var v = it.next().value;
// returns <number>

v = it.next().value;
// returns <number>

v = it.next().value;
// returns <number>

// ...
```

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 <Object>

var v = it.next().value;
// returns <number>

v = it.next().value;
// returns <number>

// ...
```

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 <Object>

var v = it.next().value;
// returns <number>

v = it.next().value;
// returns <number>

// ...
```

To translate the waveform to the right,

```javascript
var opts = {
    'period': 100,
    'offset': 1
};

var it = iterPeriodicSinc( 7, opts );
// returns <Object>

var v = it.next().value;
// returns <number>

v = it.next().value;
// returns <number>

// ...
```

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 <Object>

var v = it.next().value;
// returns <number>

v = it.next().value;
// returns <number>

var bool = it.next().done;
// returns true
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

## Notes

-   If an environment supports `Symbol.iterator`, the returned iterator is iterable.

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```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 );
}
```

</section>

<!-- /.examples -->

<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="references">

</section>

<!-- /.references -->

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<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/simulate-iter/sine-wave`][@stdlib/simulate/iter/sine-wave]</span><span class="delimiter">: </span><span class="description">create an iterator which generates a sine wave.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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