iterPeriodicSinc

Create an iterator which generates a periodic sinc waveform.

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

upper D Subscript upper N Baseline left-parenthesis x semicolon upper A right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction upper A sine left-parenthesis upper N x slash 2 right-parenthesis Over upper N sine left-parenthesis x slash 2 right-parenthesis EndFraction 2nd Column x not-equals 2 pi k for k equals 0 comma plus-or-minus 1 comma plus-or-minus 2 comma ellipsis 2nd Row 1st Column upper A left-parenthesis negative 1 right-parenthesis Superscript k left-parenthesis upper N minus 1 right-parenthesis Baseline 2nd Column x equals 2 pi k for k equals 0 comma plus-or-minus 1 comma plus-or-minus 2 comma ellipsis EndLayout

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 equals StartFraction 2 pi left-parenthesis t minus phi right-parenthesis Over tau EndFraction

and, for even N, let

x equals StartFraction 4 pi left-parenthesis t minus phi right-parenthesis Over tau EndFraction

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

upper D Subscript upper N Baseline left-parenthesis t semicolon upper A comma tau comma phi right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction upper A sine left-parenthesis upper N pi left-parenthesis t minus phi right-parenthesis slash tau right-parenthesis Over upper N sine left-parenthesis pi left-parenthesis t minus phi right-parenthesis slash tau right-parenthesis EndFraction 2nd Column t minus phi not-equals tau k for k equals 0 comma plus-or-minus 1 comma plus-or-minus 2 comma ellipsis 2nd Row 1st Column upper A left-parenthesis negative 1 right-parenthesis Superscript k left-parenthesis upper N minus 1 right-parenthesis Baseline 2nd Column t minus phi equals tau k for k equals 0 comma plus-or-minus 1 comma plus-or-minus 2 comma ellipsis EndLayout

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

upper D Subscript upper N Baseline left-parenthesis pi x semicolon upper N comma upper A right-parenthesis equals upper A dot StartFraction s i n c left-parenthesis upper N x slash 2 right-parenthesis Over s i n c left-parenthesis x slash 2 right-parenthesis EndFraction

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 );
}

See Also

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