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<html>
<head>
<title>
FFT_SERIAL - Fast Fourier Transform
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FFT_SERIAL <br> Fast Fourier Transform
</h1>
<hr>
<p>
<b>FFT_SERIAL</b>
is a MATLAB program which
demonstrates the computation of a Fast Fourier Transform.
</p>
<p>
This implementation of the Fast Fourier Transform does not run
efficiently with MATLAB. However, we can still compute some
interesting statistics about the time, the computational rate, and so on.
</p>
<p>
On an Apple PowerPC G5 with two processors, the following results were
observed:
<table border="1" align="center">
<tr>
<th>N</th><th>Iterations</th><th>Time</th><th>Time/Call</th><th>MegaFLOPS</th>
</tr>
<tr><td> 2</td><td>10,000</td><td> 1.132</td><td>5.6e-05</td><td>0.176</td></tr>
<tr><td> 4</td><td>10,000</td><td> 2.264</td><td>1.1e-04</td><td>0.353</td></tr>
<tr><td> 8</td><td>10,000</td><td> 3.458</td><td>1.7e-04</td><td>0.693</td></tr>
<tr><td> 16</td><td>10,000</td><td> 6.064</td><td>3.0e-04</td><td>1.055</td></tr>
<tr><td> 32</td><td> 1,000</td><td> 1.066</td><td>5.3e-04</td><td>1.499</td></tr>
<tr><td> 64</td><td> 1,000</td><td> 2.326</td><td>1.1e-03</td><td>1.650</td></tr>
<tr><td> 128</td><td> 1,000</td><td> 5.122</td><td>2.5e-03</td><td>1.749</td></tr>
<tr><td> 256</td><td> 1,000</td><td>11.959</td><td>5.9e-03</td><td>1.712</td></tr>
<tr><td> 512</td><td> 100</td><td> 2.932</td><td>1.4e-02</td><td>1.571</td></tr>
<tr><td> 1024</td><td> 100</td><td>19.697</td><td>9.8e-02</td><td>0.519</td></tr>
</table>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FFT_SERIAL</b> is available in
<a href = "../../c_src/fft_serial/fft_serial.html">a C version</a> and
<a href = "../../cpp_src/fft_serial/fft_serial.html">a C++ version</a> and
<a href = "../../f77_src/fft_serial/fft_serial.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fft_serial/fft_serial.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fft_serial/fft_serial.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/fire_serial/fire_serial.html">
FIRE_SERIAL</a>,
a MATLAB program which
simulates a forest fire over a rectangular array of trees,
starting at a single random location. It is intended as a starting
point for the development of a parallel version.
</p>
<p>
<a href = "../../m_src/heated_plate/heated_plate.html">
HEATED_PLATE</a>,
a MATLAB program which
solves the steady (time independent) heat equation in a 2D
rectangular region, and is intended as
a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../m_src/linpack_bench/linpack_bench.html">
LINPACK_BENCH</a>,
a MATLAB program which
measures the time taken by <b>LINPACK</b> to solve a particular linear system.
</p>
<p>
<a href = "../../m_src/linpack_bench_backslash/linpack_bench_backslash.html">
LINPACK_BENCH_BACKSLASH</a>,
a MATLAB program which
measures the time taken by <b>LINPACK</b> to solve a particular linear system,
and uses MATLAB's builtin "backslash" operator to do the solving.
</p>
<p>
<a href = "../../m_src/matlab_parallel/matlab_parallel.html">
MATLAB_PARALLEL</a>,
MATLAB programs which
illustrate "local" parallel programming on a single computer
with MATLAB's Parallel Computing Toolbox.
</p>
<p>
<a href = "../../m_src/md/md.html">
MD</a>,
a MATLAB program which
carries out a molecular dynamics simulation,
and is intended as a starting point for developing a parallel version
using OpenMP.
<p>
<p>
<a href = "../../m_src/poisson_serial/poisson_serial.html">
POISSON_SERIAL</a>,
a MATLAB program which
computes an approximate solution to the Poisson equation in a rectangle,
and is intended as the starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../m_src/power_method/power_method.html">
POWER_METHOD</a>,
a MATLAB library which
carries out the power method for finding a dominant eigenvalue
and its eigenvector.
</p>
<p>
<a href = "../../m_src/prime_serial/prime_serial.html">
PRIME_SERIAL</a>,
a MATLAB program which
counts the number of primes between 1 and N,
intended as a starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../m_src/quad_serial/quad_serial.html">
QUAD_SERIAL</a>,
a MATLAB program which
approximates an integral using a quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<p>
<a href = "../../m_src/satisfy/satisfy.html">
SATISFY</a>,
a MATLAB program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem.
</p>
<p>
<a href = "../../m_src/search_serial/search_serial.html">
SEARCH_SERIAL</a>,
a MATLAB program which
searches the integers from A to B for a value J such that F(J) = C.
this version of the program is intended as a starting point for
a parallel approach.
</p>
<p>
<a href = "../../m_src/timer/timer.html">
TIMER</a>,
MATLAB programs which
demonstrate how to compute CPU time or elapsed time.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Wesley Petersen, Peter Arbenz, <br>
Introduction to Parallel Computing - A practical guide with examples in C,<br>
Oxford University Press,<br>
ISBN: 0-19-851576-6,<br>
LC: QA76.58.P47.
</li>
<li>
Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan,
Jeff McDonald, Ramesh Menon,<br>
Parallel Programming in OpenMP,<br>
Morgan Kaufmann, 2001,<br>
ISBN: 1-55860-671-8,<br>
LC: QA76.642.P32.
</li>
<li>
Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,<br>
Using OpenMP: Portable Shared Memory Parallel Processing,<br>
MIT Press, 2007,<br>
ISBN13: 978-0262533027,<br>
LC: QA76.642.C49.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fft_serial.m">fft_serial.m</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fft_serial_output.txt">fft_serial_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 16 May 2009.
</i>
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