<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html> <head> <!-- Generated by HsColour, http://www.cs.york.ac.uk/fp/darcs/hscolour/ --> <title>src/ForSyDe/Shallow/DFT.hs</title> <link type='text/css' rel='stylesheet' href='hscolour.css' /> </head> <body> <pre><a name="line-1"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span> <a name="line-2"></a><span class='hs-comment'>-- |</span> <a name="line-3"></a><span class='hs-comment'>-- Module : ForSyDe.DFT</span> <a name="line-4"></a><span class='hs-comment'>-- Copyright : (c) SAM Group, KTH/ICT/ECS 2007-2008</span> <a name="line-5"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span> <a name="line-6"></a><span class='hs-comment'>-- </span> <a name="line-7"></a><span class='hs-comment'>-- Maintainer : forsyde-dev@ict.kth.se</span> <a name="line-8"></a><span class='hs-comment'>-- Stability : experimental</span> <a name="line-9"></a><span class='hs-comment'>-- Portability : portable</span> <a name="line-10"></a><span class='hs-comment'>--</span> <a name="line-11"></a><span class='hs-comment'>-- This module includes the standard Discrete Fourier Transform (DFT)</span> <a name="line-12"></a><span class='hs-comment'>-- function, and a fast Fourier transform (FFT) algorithm, for</span> <a name="line-13"></a><span class='hs-comment'>-- computing the DFT, when the input vectors' length is a power of 2.</span> <a name="line-14"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span> <a name="line-15"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>Shallow</span><span class='hs-varop'>.</span><span class='hs-conid'>DFT</span><span class='hs-layout'>(</span><span class='hs-varid'>dft</span><span class='hs-layout'>,</span> <span class='hs-varid'>fft</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-16"></a> <a name="line-17"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>Shallow</span><span class='hs-varop'>.</span><span class='hs-conid'>Vector</span> <a name="line-18"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Complex</span> <a name="line-19"></a> <a name="line-20"></a><a name="dft"></a><span class='hs-comment'>-- | The function 'dft' performs a standard Discrete Fourier Transformation</span> <a name="line-21"></a><span class='hs-definition'>dft</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Vector</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-conid'>Double</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Vector</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-conid'>Double</span><span class='hs-layout'>)</span> <a name="line-22"></a><span class='hs-definition'>dft</span> <span class='hs-varid'>bigN</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>bigN</span> <span class='hs-varop'>==</span> <span class='hs-layout'>(</span><span class='hs-varid'>lengthV</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapV</span> <span class='hs-layout'>(</span><span class='hs-varid'>bigX_k</span> <span class='hs-varid'>bigN</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>nVector</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <a name="line-23"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"DFT: Vector has not the right size!"</span> <a name="line-24"></a> <span class='hs-keyword'>where</span> <a name="line-25"></a> <span class='hs-varid'>nVector</span> <span class='hs-varid'>x'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iterateV</span> <span class='hs-layout'>(</span><span class='hs-varid'>lengthV</span> <span class='hs-varid'>x'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <a name="line-26"></a> <span class='hs-varid'>bigX_k</span> <span class='hs-varid'>bigN'</span> <span class='hs-varid'>x'</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sumV</span> <span class='hs-layout'>(</span><span class='hs-varid'>zipWithV</span> <span class='hs-layout'>(</span><span class='hs-varop'>*</span><span class='hs-layout'>)</span> <span class='hs-varid'>x'</span> <span class='hs-layout'>(</span><span class='hs-varid'>bigW'</span> <span class='hs-varid'>k</span> <span class='hs-varid'>bigN'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-27"></a> <span class='hs-varid'>bigW'</span> <span class='hs-varid'>k'</span> <span class='hs-varid'>bigN'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapV</span> <span class='hs-layout'>(</span><span class='hs-varop'>**</span> <span class='hs-varid'>k'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>mapV</span> <span class='hs-varid'>cis</span> <span class='hs-layout'>(</span><span class='hs-varid'>fullcircle</span> <span class='hs-varid'>bigN'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-28"></a> <span class='hs-varid'>sumV</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldlV</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0</span><span class='hs-conop'>:+</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <a name="line-29"></a> <a name="line-30"></a><a name="fullcircle"></a><span class='hs-definition'>fullcircle</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Vector</span> <span class='hs-conid'>Double</span> <a name="line-31"></a><span class='hs-definition'>fullcircle</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fullcircle1</span> <span class='hs-num'>0</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-varid'>n</span> <a name="line-32"></a> <span class='hs-keyword'>where</span> <a name="line-33"></a> <span class='hs-varid'>fullcircle1</span> <span class='hs-varid'>l</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n'</span> <a name="line-34"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>l</span> <span class='hs-varop'>==</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>NullV</span> <a name="line-35"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>2</span><span class='hs-varop'>*</span><span class='hs-varid'>pi</span><span class='hs-varop'>*</span><span class='hs-varid'>l</span><span class='hs-varop'>/</span><span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>n'</span><span class='hs-layout'>)</span> <a name="line-36"></a> <span class='hs-conop'>:></span> <span class='hs-varid'>fullcircle1</span> <span class='hs-layout'>(</span><span class='hs-varid'>l</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n'</span> <a name="line-37"></a> <a name="line-38"></a><a name="fft"></a><span class='hs-comment'>-- | The function 'fft' implements a fast Fourier transform (FFT) algorithm, for computing the DFT, when the size N is a power of 2.</span> <a name="line-39"></a><span class='hs-definition'>fft</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Vector</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-conid'>Double</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Vector</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-conid'>Double</span><span class='hs-layout'>)</span> <a name="line-40"></a><span class='hs-definition'>fft</span> <span class='hs-varid'>bigN</span> <span class='hs-varid'>xv</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>bigN</span> <span class='hs-varop'>==</span> <span class='hs-layout'>(</span><span class='hs-varid'>lengthV</span> <span class='hs-varid'>xv</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapV</span> <span class='hs-layout'>(</span><span class='hs-varid'>bigX</span> <span class='hs-varid'>xv</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>kVector</span> <span class='hs-varid'>bigN</span><span class='hs-layout'>)</span> <a name="line-41"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"FFT: Vector has not the right size!"</span> <a name="line-42"></a> <a name="line-43"></a><a name="kVector"></a><span class='hs-definition'>kVector</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Vector</span> <span class='hs-varid'>b</span> <a name="line-44"></a><span class='hs-definition'>kVector</span> <span class='hs-varid'>bigN</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iterateV</span> <span class='hs-varid'>bigN</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <a name="line-45"></a> <a name="line-46"></a> <a name="line-47"></a><a name="bigX"></a><span class='hs-definition'>bigX</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-conid'>Double</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Complex</span> <span class='hs-conid'>Double</span> <a name="line-48"></a><span class='hs-definition'>bigX</span> <span class='hs-layout'>(</span><span class='hs-varid'>x0</span><span class='hs-conop'>:></span><span class='hs-varid'>x1</span><span class='hs-conop'>:></span><span class='hs-conid'>NullV</span><span class='hs-layout'>)</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>even</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x0</span> <span class='hs-varop'>+</span> <span class='hs-varid'>x1</span> <span class='hs-varop'>*</span> <span class='hs-varid'>bigW</span> <span class='hs-num'>2</span> <span class='hs-num'>0</span> <a name="line-49"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>odd</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x0</span> <span class='hs-comment'>-</span> <span class='hs-varid'>x1</span> <span class='hs-varop'>*</span> <span class='hs-varid'>bigW</span> <span class='hs-num'>2</span> <span class='hs-num'>0</span> <a name="line-50"></a><span class='hs-definition'>bigX</span> <span class='hs-varid'>xv</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bigF_even</span> <span class='hs-varid'>k</span> <span class='hs-varop'>+</span> <span class='hs-varid'>bigF_odd</span> <span class='hs-varid'>k</span> <span class='hs-varop'>*</span> <span class='hs-varid'>bigW</span> <span class='hs-varid'>bigN</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <a name="line-51"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>bigF_even</span> <span class='hs-varid'>k'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bigX</span> <span class='hs-layout'>(</span><span class='hs-varid'>evens</span> <span class='hs-varid'>xv</span><span class='hs-layout'>)</span> <span class='hs-varid'>k'</span> <a name="line-52"></a> <span class='hs-varid'>bigF_odd</span> <span class='hs-varid'>k'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bigX</span> <span class='hs-layout'>(</span><span class='hs-varid'>odds</span> <span class='hs-varid'>xv</span><span class='hs-layout'>)</span> <span class='hs-varid'>k'</span> <a name="line-53"></a> <span class='hs-varid'>bigN</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lengthV</span> <span class='hs-varid'>xv</span> <a name="line-54"></a> <a name="line-55"></a><a name="bigW"></a><span class='hs-definition'>bigW</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Complex</span> <span class='hs-conid'>Double</span> <a name="line-56"></a><span class='hs-definition'>bigW</span> <span class='hs-varid'>bigN</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cis</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>2</span> <span class='hs-varop'>*</span> <span class='hs-varid'>pi</span> <span class='hs-varop'>*</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-varop'>/</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>bigN</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-57"></a> <a name="line-58"></a><a name="evens"></a><span class='hs-definition'>evens</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Vector</span> <span class='hs-varid'>a</span> <a name="line-59"></a><span class='hs-definition'>evens</span> <span class='hs-conid'>NullV</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>NullV</span> <a name="line-60"></a><span class='hs-definition'>evens</span> <span class='hs-layout'>(</span><span class='hs-varid'>v1</span><span class='hs-conop'>:></span><span class='hs-conid'>NullV</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v1</span> <span class='hs-conop'>:></span> <span class='hs-conid'>NullV</span> <a name="line-61"></a><span class='hs-definition'>evens</span> <span class='hs-layout'>(</span><span class='hs-varid'>v1</span><span class='hs-conop'>:></span><span class='hs-keyword'>_</span><span class='hs-conop'>:></span><span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v1</span> <span class='hs-conop'>:></span> <span class='hs-varid'>evens</span> <span class='hs-varid'>v</span> <a name="line-62"></a> <a name="line-63"></a><a name="odds"></a><span class='hs-definition'>odds</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Vector</span> <span class='hs-varid'>a</span> <a name="line-64"></a><span class='hs-definition'>odds</span> <span class='hs-conid'>NullV</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>NullV</span> <a name="line-65"></a><span class='hs-definition'>odds</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:></span><span class='hs-conid'>NullV</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>NullV</span> <a name="line-66"></a><span class='hs-definition'>odds</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:></span><span class='hs-varid'>v2</span><span class='hs-conop'>:></span><span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v2</span> <span class='hs-conop'>:></span> <span class='hs-varid'>odds</span> <span class='hs-varid'>v</span> <a name="line-67"></a> <a name="line-68"></a> <a name="line-69"></a> <a name="line-70"></a> <a name="line-71"></a> </pre></body> </html>
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