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iterPeriodicSinc

Create an iterator which generates a periodic sinc waveform.

The periodic sinc function, also known as the Dirichlet function, is defined as

$$D_N(x; A) = \begin{cases}\frac{A\sin(Nx/2)} {N\sin(x/2)} & x \neq 2\pi k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \\ A (-1)^{k(N-1)} & x = 2\pi k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \end{cases}$$

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 function as a function of a discrete iteration number t and the waveform period τ, for odd N, let

$$x = \frac{2\pi (t-\varphi)}{\tau}$$

and, for even N, let

$$x = \frac{4\pi (t-\varphi)}{\tau}$$

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 function as

$$D_N(t; A, \tau, \varphi) = \begin{cases}\frac{A\sin(N\pi(t-\varphi)/\tau)} {N\sin(\pi (t-\varphi)/\tau)} & t-\varphi \neq \tau k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \\ A (-1)^{k(N-1)} & t-\varphi = \tau k\ \textrm{for}\ k = 0, \pm 1, \pm 2, \ldots \end{cases}$$

For even N, we can express the periodic sinc function similarly.

Note that the periodic sinc can be equivalently expressed as a function of the sinc function

$$D_N(\pi x; N, A) = A \cdot \frac{\mathop{\mathrm{sinc}}(Nx/2)} {\mathop{\mathrm{sinc}}(x/2)}$$

Installation

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 available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

var iterPeriodicSinc = require( '@stdlib/simulate-iter-periodic-sinc' );

iterPeriodicSinc( n[, options] )

Returns an iterator which generates a periodic sinc waveform of order n.

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.

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,

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,

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.

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

Notes

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

Examples

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 );
}

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See Also

• @stdlib/simulate-iter/sine-wave: create an iterator which generates a sine wave.

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

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