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reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["cardinal","diric","dirichlet","iterate","iteration","iterator","javascript","node","node-js","nodejs","periodic","processing","signal","simulate","simulation","sinc","sine","stdlib","wave","waveform"],"created_at":"2025-05-14T17:13:29.729Z","updated_at":"2026-02-17T22:01:49.310Z","avatar_url":"https://github.com/stdlib-js.png","language":"JavaScript","readme":"\u003c!--\n\n@license Apache-2.0\n\nCopyright (c) 2019 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n--\u003e\n\n\n\u003cdetails\u003e\n  \u003csummary\u003e\n    About stdlib...\n  \u003c/summary\u003e\n  \u003cp\u003eWe believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.\u003c/p\u003e\n  \u003cp\u003eThe library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.\u003c/p\u003e\n  \u003cp\u003eWhen you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.\u003c/p\u003e\n  \u003cp\u003eTo join us in bringing numerical computing to the web, get started by checking us out on \u003ca href=\"https://github.com/stdlib-js/stdlib\"\u003eGitHub\u003c/a\u003e, and please consider \u003ca href=\"https://opencollective.com/stdlib\"\u003efinancially supporting stdlib\u003c/a\u003e. We greatly appreciate your continued support!\u003c/p\u003e\n\u003c/details\u003e\n\n# iterPeriodicSinc\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \u003c!-- [![dependencies][dependencies-image]][dependencies-url] --\u003e\n\n\u003e Create an iterator which generates a periodic [sinc][@stdlib/math/base/special/sinc] waveform.\n\n\u003c!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"intro\"\u003e\n\nThe periodic [sinc][@stdlib/math/base/special/sinc] function, also known as the Dirichlet function, is defined as\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:periodic_sinc\" align=\"center\" raw=\"D_N(x; A) = \\begin{cases}\\frac{A\\sin(Nx/2)} {N\\sin(x/2)} \u0026 x \\neq 2\\pi k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots  \\\\ A (-1)^{k(N-1)} \u0026 x = 2\\pi k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots \\end{cases}\" alt=\"Periodic sinc function.\"\u003e --\u003e\n\n```math\nD_N(x; A) = \\begin{cases}\\frac{A\\sin(Nx/2)} {N\\sin(x/2)} \u0026 x \\neq 2\\pi k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots  \\\\ A (-1)^{k(N-1)} \u0026 x = 2\\pi k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots \\end{cases}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"D_N(x; A) = \\begin{cases}\\frac{A\\sin(Nx/2)} {N\\sin(x/2)} \u0026amp; x \\neq 2\\pi k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots  \\\\ A (-1)^{k(N-1)} \u0026amp; x = 2\\pi k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots \\end{cases}\" data-equation=\"eq:periodic_sinc\"\u003e\n    \u003cimg 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.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere `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`.\n\nTo 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\n\n\u003c!-- \u003cequation 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.\"\u003e --\u003e\n\n```math\nx = \\frac{2\\pi (t-\\varphi)}{\\tau}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"x = \\frac{2\\pi (t-\\varphi)}{\\tau}\" data-equation=\"eq:periodic_sinc_substitution_odd\"\u003e\n    \u003cimg 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.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nand, for even `N`, let\n\n\u003c!-- \u003cequation 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.\"\u003e --\u003e\n\n```math\nx = \\frac{4\\pi (t-\\varphi)}{\\tau}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"x = \\frac{4\\pi (t-\\varphi)}{\\tau}\" data-equation=\"eq:periodic_sinc_substitution_even\"\u003e\n    \u003cimg 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.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere `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\n\n\u003c!-- \u003cequation 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)} \u0026 t-\\varphi \\neq \\tau k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots  \\\\ A (-1)^{k(N-1)} \u0026 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.\"\u003e --\u003e\n\n```math\nD_N(t; A, \\tau, \\varphi) = \\begin{cases}\\frac{A\\sin(N\\pi(t-\\varphi)/\\tau)} {N\\sin(\\pi (t-\\varphi)/\\tau)} \u0026 t-\\varphi \\neq \\tau k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots  \\\\ A (-1)^{k(N-1)} \u0026 t-\\varphi = \\tau k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots \\end{cases}\n```\n\n\u003c!-- \u003cdiv 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)} \u0026amp; t-\\varphi \\neq \\tau k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots  \\\\ A (-1)^{k(N-1)} \u0026amp; t-\\varphi = \\tau k\\ \\textrm{for}\\ k = 0, \\pm 1, \\pm 2, \\ldots \\end{cases}\" data-equation=\"eq:periodic_sinc_in_terms_of_period\"\u003e\n    \u003cimg 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.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nFor even `N`, we can express the periodic [sinc][@stdlib/math/base/special/sinc] function similarly.\n\nNote 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\n\n\u003c!-- \u003cequation 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.\"\u003e --\u003e\n\n```math\nD_N(\\pi x; N, A) = A \\cdot \\frac{\\mathop{\\mathrm{sinc}}(Nx/2)} {\\mathop{\\mathrm{sinc}}(x/2)}\n```\n\n\u003c!-- \u003cdiv 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\"\u003e\n    \u003cimg 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.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\n\u003c!-- TODO: add a figure showing a periodic sinc waveform --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003c!-- Package usage documentation. --\u003e\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/simulate-iter-periodic-sinc\n```\n\nAlternatively,\n\n-   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]).\n-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).\n-   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]).\n\nThe [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.\n\nTo 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.\n\n\u003c/section\u003e\n\n\u003csection class=\"usage\"\u003e\n\n## Usage\n\n```javascript\nvar iterPeriodicSinc = require( '@stdlib/simulate-iter-periodic-sinc' );\n```\n\n#### iterPeriodicSinc( n\\[, options] )\n\nReturns an iterator which generates a periodic [sinc][@stdlib/math/base/special/sinc] waveform of order `n`.\n\n```javascript\nvar it = iterPeriodicSinc( 7 );\n// returns \u003cObject\u003e\n\nvar v = it.next().value;\n// returns \u003cnumber\u003e\n\nv = it.next().value;\n// returns \u003cnumber\u003e\n\nv = it.next().value;\n// returns \u003cnumber\u003e\n\n// ...\n```\n\nThe returned iterator protocol-compliant object has the following properties:\n\n-   **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.\n-   **return**: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.\n\nThe function supports the following `options`:\n\n-   **period**: period (i.e., the number of iterations before a waveform repeats). Default: `100`.\n-   **amplitude**: peak amplitude. Default: `1.0`.\n-   **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`.\n-   **iter**: number of iterations. Default: `1e308`.\n\nBy default, the function returns an iterator which generates a waveform that repeats every `100` iterations. To specify an alternative period, set the `period` option.\n\n```javascript\nvar opts = {\n    'period': 1000\n};\n\nvar it = iterPeriodicSinc( 7, opts );\n// returns \u003cObject\u003e\n\nvar v = it.next().value;\n// returns \u003cnumber\u003e\n\nv = it.next().value;\n// returns \u003cnumber\u003e\n\n// ...\n```\n\nTo 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,\n\n```javascript\nvar opts = {\n    'period': 100,\n    'offset': -1\n};\n\nvar it = iterPeriodicSinc( 7, opts );\n// returns \u003cObject\u003e\n\nvar v = it.next().value;\n// returns \u003cnumber\u003e\n\nv = it.next().value;\n// returns \u003cnumber\u003e\n\n// ...\n```\n\nTo translate the waveform to the right,\n\n```javascript\nvar opts = {\n    'period': 100,\n    'offset': 1\n};\n\nvar it = iterPeriodicSinc( 7, opts );\n// returns \u003cObject\u003e\n\nvar v = it.next().value;\n// returns \u003cnumber\u003e\n\nv = it.next().value;\n// returns \u003cnumber\u003e\n\n// ...\n```\n\nBy default, the function returns an infinite iterator (i.e., an iterator which never ends). To limit the number of iterations, set the `iter` option.\n\n```javascript\nvar opts = {\n    'iter': 2\n};\nvar it = iterPeriodicSinc( 7, opts );\n// returns \u003cObject\u003e\n\nvar v = it.next().value;\n// returns \u003cnumber\u003e\n\nv = it.next().value;\n// returns \u003cnumber\u003e\n\nvar bool = it.next().done;\n// returns true\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003c!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"notes\"\u003e\n\n## Notes\n\n-   If an environment supports `Symbol.iterator`, the returned iterator is iterable.\n\n\u003c/section\u003e\n\n\u003c!-- /.notes --\u003e\n\n\u003c!-- Package usage examples. --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar iterPeriodicSinc = require( '@stdlib/simulate-iter-periodic-sinc' );\n\n// Create an iterator:\nvar opts = {\n    'period': 100,\n    'amplitude': 10.0,\n    'offset': -50,\n    'iter': 100\n};\nvar it = iterPeriodicSinc( 7, opts );\n\n// Perform manual iteration...\nvar v;\nwhile ( true ) {\n    v = it.next();\n    if ( v.done ) {\n        break;\n    }\n    console.log( v.value );\n}\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c!-- 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. --\u003e\n\n\u003csection class=\"references\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.references --\u003e\n\n\u003c!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --\u003e\n\n\u003csection class=\"related\"\u003e\n\n* * *\n\n## See Also\n\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/simulate-iter/sine-wave`][@stdlib/simulate/iter/sine-wave]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecreate an iterator which generates a sine wave.\u003c/span\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.related --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\n\u003csection class=\"main-repo\" \u003e\n\n* * *\n\n## Notice\n\nThis 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.\n\nFor 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].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright \u0026copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n\u003c/section\u003e\n\n\u003c!-- /.stdlib --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"links\"\u003e\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/simulate-iter-periodic-sinc.svg\n[npm-url]: https://npmjs.org/package/@stdlib/simulate-iter-periodic-sinc\n\n[test-image]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/actions/workflows/test.yml/badge.svg?branch=v0.2.3\n[test-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/actions/workflows/test.yml?query=branch:v0.2.3\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/simulate-iter-periodic-sinc/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/simulate-iter-periodic-sinc?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/simulate-iter-periodic-sinc.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/simulate-iter-periodic-sinc/main\n\n--\u003e\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/tree/deno\n[deno-readme]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/tree/umd\n[umd-readme]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/tree/esm\n[esm-readme]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/simulate-iter-periodic-sinc/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/simulate-iter-periodic-sinc/main/LICENSE\n\n[@stdlib/math/base/special/sinc]: https://github.com/stdlib-js/math-base-special-sinc\n\n\u003c!-- \u003crelated-links\u003e --\u003e\n\n[@stdlib/simulate/iter/sine-wave]: https://github.com/stdlib-js/simulate-iter-sine-wave\n\n\u003c!-- \u003c/related-links\u003e --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fsimulate-iter-periodic-sinc","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fsimulate-iter-periodic-sinc","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fsimulate-iter-periodic-sinc/lists"}