Mercurial > hg > js-dsp-test

annotate fft/fftw/fftw-3.3.4/doc/html/Complex-numbers.html @ 40:223f770b5341 kissfft-double tip

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Try a double-precision kissfft
author Chris Cannam
date Wed, 07 Sep 2016 10:40:32 +0100
parents 26056e866c29
children
rev   line source
Chris@19 1 <html lang="en">
Chris@19 2 <head>
Chris@19 3 <title>Complex numbers - FFTW 3.3.4</title>
Chris@19 4 <meta http-equiv="Content-Type" content="text/html">
Chris@19 5 <meta name="description" content="FFTW 3.3.4">
Chris@19 6 <meta name="generator" content="makeinfo 4.13">
Chris@19 7 <link title="Top" rel="start" href="index.html#Top">
Chris@19 8 <link rel="up" href="Data-Types-and-Files.html#Data-Types-and-Files" title="Data Types and Files">
Chris@19 9 <link rel="prev" href="Data-Types-and-Files.html#Data-Types-and-Files" title="Data Types and Files">
Chris@19 10 <link rel="next" href="Precision.html#Precision" title="Precision">
Chris@19 11 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
Chris@19 12 <!--
Chris@19 13 This manual is for FFTW
Chris@19 14 (version 3.3.4, 20 September 2013).
Chris@19 15
Chris@19 16 Copyright (C) 2003 Matteo Frigo.
Chris@19 17
Chris@19 18 Copyright (C) 2003 Massachusetts Institute of Technology.
Chris@19 19
Chris@19 20 Permission is granted to make and distribute verbatim copies of
Chris@19 21 this manual provided the copyright notice and this permission
Chris@19 22 notice are preserved on all copies.
Chris@19 23
Chris@19 24 Permission is granted to copy and distribute modified versions of
Chris@19 25 this manual under the conditions for verbatim copying, provided
Chris@19 26 that the entire resulting derived work is distributed under the
Chris@19 27 terms of a permission notice identical to this one.
Chris@19 28
Chris@19 29 Permission is granted to copy and distribute translations of this
Chris@19 30 manual into another language, under the above conditions for
Chris@19 31 modified versions, except that this permission notice may be
Chris@19 32 stated in a translation approved by the Free Software Foundation.
Chris@19 33 -->
Chris@19 34 <meta http-equiv="Content-Style-Type" content="text/css">
Chris@19 35 <style type="text/css"><!--
Chris@19 36 pre.display { font-family:inherit }
Chris@19 37 pre.format { font-family:inherit }
Chris@19 38 pre.smalldisplay { font-family:inherit; font-size:smaller }
Chris@19 39 pre.smallformat { font-family:inherit; font-size:smaller }
Chris@19 40 pre.smallexample { font-size:smaller }
Chris@19 41 pre.smalllisp { font-size:smaller }
Chris@19 42 span.sc { font-variant:small-caps }
Chris@19 43 span.roman { font-family:serif; font-weight:normal; }
Chris@19 44 span.sansserif { font-family:sans-serif; font-weight:normal; }
Chris@19 45 --></style>
Chris@19 46 </head>
Chris@19 47 <body>
Chris@19 48 <div class="node">
Chris@19 49 <a name="Complex-numbers"></a>
Chris@19 50 <p>
Chris@19 51 Next:&nbsp;<a rel="next" accesskey="n" href="Precision.html#Precision">Precision</a>,
Chris@19 52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>,
Chris@19 53 Up:&nbsp;<a rel="up" accesskey="u" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>
Chris@19 54 <hr>
Chris@19 55 </div>
Chris@19 56
Chris@19 57 <h4 class="subsection">4.1.1 Complex numbers</h4>
Chris@19 58
Chris@19 59 <p>The default FFTW interface uses <code>double</code> precision for all
Chris@19 60 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
Chris@19 61 complex numbers as:
Chris@19 62
Chris@19 63 <pre class="example"> typedef double fftw_complex[2];
Chris@19 64 </pre>
Chris@19 65 <p><a name="index-fftw_005fcomplex-139"></a>
Chris@19 66 Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
Chris@19 67 element holds the imaginary part.
Chris@19 68
Chris@19 69 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
Chris@19 70 supports the C99 revision of the ANSI C standard, you can use C's new
Chris@19 71 native complex type (which is binary-compatible with the typedef above).
Chris@19 72 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
Chris@19 73 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
Chris@19 74 complex type and you can manipulate it with ordinary arithmetic
Chris@19 75 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
Chris@19 76 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
Chris@19 77 imaginary unit);
Chris@19 78 <a name="index-C99-140"></a>
Chris@19 79
Chris@19 80 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
Chris@19 81 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
Chris@19 82 committee has recently agreed to mandate that the storage format used
Chris@19 83 for this type be binary-compatible with the C99 type, i.e. an array
Chris@19 84 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
Chris@19 85 parts. (See report
Chris@19 86 <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf WG21/N1388</a>.) Although not part of the official standard as of this
Chris@19 87 writing, the proposal stated that: &ldquo;This solution has been tested with
Chris@19 88 all current major implementations of the standard library and shown to
Chris@19 89 be working.&rdquo; To the extent that this is true, if you have a variable
Chris@19 90 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
Chris@19 91 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
Chris@19 92 <a name="index-C_002b_002b-141"></a><a name="index-portability-142"></a>
Chris@19 93 <!-- =========> -->
Chris@19 94
Chris@19 95 </body></html>
Chris@19 96