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sinqi

Initialize a workspace array for performing a quarter-wave sine transform.

Installation

npm install @stdlib/fft-base-fftpack-sinqi

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 sinqi = require( '@stdlib/fft-base-fftpack-sinqi' );

sinqi( N, workspace, strideW, offsetW )

Initializes a workspace array for performing a quarter-wave sine transform.

var Float64Array = require( '@stdlib/array-float64' );

var N = 8;
var workspace = new Float64Array( ( 3*N ) + 34 );

var out = sinqi( N, workspace, 1, 0 );
// returns <Float64Array>

var bool = ( out === workspace );
// returns true

var cosineTable = workspace.slice( 0, N );
// returns <Float64Array>[ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ]

var twiddleFactors = workspace.slice( 2*N, 3*N );
// returns <Float64Array>[ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ]

var factors = workspace.slice( 3*N, ( 3*N ) + 4 );
// returns <Float64Array>[ 8, 2, 2, 4 ]

The function accepts the following arguments:

• N: length of the sequence to transform.
• workspace: workspace array.
• strideW: stride length for workspace.
• offsetW: starting index for workspace.

Notes

• The workspace array is divided into four sections:

          size = N              N                   N          2+ceil(log2(N)/2)
              ↓                 ↓                   ↓                  ↓
      | cosine table | scratch / workspace | twiddle factors | radix factor table |
              ↑                 ↑                   ↑                  ↑
  i = 0      ...     N         ...        2N       ...      3N        ...
  

  • cosine table: a table of precomputed cosine coefficients used by quarter-wave sine transforms.
  • scratch/workspace: used as a scratch space when performing transforms. This section is not updated during initialization.
  • twiddle factors: a table of reusable complex-exponential constants stored as cosine/sine pairs.
  • radix factor table: a table containing the sequence length N, the number of factors into which N was decomposed, and the individual integer radix factors.

• In general, a workspace array should have 3N + 34 indexed elements (as log2(N)/2 ≤ 32 for all 2^64). During initialization, only the sections for storing the cosine coefficients, twiddle factors, and the factorization of N are updated.

• The radix factor table is comprised as follows:

  | sequence_length | number_of_factors | integer_factors |
  

Examples

var Float64Array = require( '@stdlib/array-float64' );
var zeroTo = require( '@stdlib/array-zero-to' );
var logEach = require( '@stdlib/console-log-each' );
var sinqi = require( '@stdlib/fft-base-fftpack-sinqi' );

var N = 8;
var workspace = new Float64Array( ( 3*N ) + 34 );

sinqi( N, workspace, 1, 0 );
console.log( 'Sequence length: %d', N );

console.log( 'Cosine table:' );
var idx = zeroTo( N, 'generic' );
logEach( '  workspace[ %d ] = %0.4f', idx, workspace.slice( 0, N ) );

console.log( 'Twiddle factors:' );
idx = zeroTo( N, 'generic' );
logEach( '  workspace[ %d ] = %0.4f', idx, workspace.slice( 2*N, 3*N ) );

console.log( 'Factorization:' );
var nf = workspace[ (3*N)+1 ];

console.log( '  number of factors: %d', nf );
idx = zeroTo( nf, 'generic' );
logEach( '  factor[ %d ]: %d', idx, workspace.slice( (3*N)+2, (3*N)+2+nf ) );

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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

Copyright © 2016-2026. The Stdlib Authors.