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<title>src/ForSyDe/FIR.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE TemplateHaskell, RelaxedPolyRec, PatternGuards #-}</span>
<a name="line-2"></a><span class='hs-comment'>-- The PatternGuards are used to hush innapropiate compiler warnings</span>
<a name="line-3"></a><span class='hs-comment'>-- see <a href="http://hackage.haskell.org/trac/ghc/ticket/2017">http://hackage.haskell.org/trac/ghc/ticket/2017</a></span>
<a name="line-4"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-5"></a><span class='hs-comment'>-- |</span>
<a name="line-6"></a><span class='hs-comment'>-- Module : ForSyDe.FIR</span>
<a name="line-7"></a><span class='hs-comment'>-- Copyright : (c) SAM Group, KTH/ICT/ECS 2007-2008</span>
<a name="line-8"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-9"></a><span class='hs-comment'>-- </span>
<a name="line-10"></a><span class='hs-comment'>-- Maintainer : forsyde-dev@ict.kth.se</span>
<a name="line-11"></a><span class='hs-comment'>-- Stability : experimental</span>
<a name="line-12"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-13"></a><span class='hs-comment'>--</span>
<a name="line-14"></a><span class='hs-comment'>-- This module implements FIR filters for the synchronous computational model.</span>
<a name="line-15"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-16"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>FIR</span> <span class='hs-layout'>(</span><span class='hs-varid'>fir</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-17"></a>
<a name="line-18"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>Ids</span>
<a name="line-19"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>Signal</span>
<a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>Process</span>
<a name="line-21"></a>
<a name="line-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Num</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span><span class='hs-layout'>,</span> <span class='hs-conid'>Pos</span><span class='hs-layout'>)</span>
<a name="line-23"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Param</span><span class='hs-varop'>.</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'>++</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-24"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Param</span><span class='hs-varop'>.</span><span class='hs-conid'>FSVec</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>V</span>
<a name="line-25"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Typeable</span>
<a name="line-26"></a>
<a name="line-27"></a><span class='hs-comment'>-- | </span>
<a name="line-28"></a><span class='hs-comment'>-- All kinds of FIR-filters can now be modeled by means of 'fir'. The</span>
<a name="line-29"></a><span class='hs-comment'>-- only argument needed is the list of coefficients, which is given as</span>
<a name="line-30"></a><span class='hs-comment'>-- a vector of any size. To illustrate this, an 8-th order band pass</span>
<a name="line-31"></a><span class='hs-comment'>-- filter is modeled as follows.</span>
<a name="line-32"></a><span class='hs-comment'>--</span>
<a name="line-33"></a><span class='hs-comment'>-- > bp = fir "fir Id" $(vectorTH [0.06318761339784, 0.08131651217682, 0.09562326700432, </span>
<a name="line-34"></a><span class='hs-comment'>-- > 0.10478344432968, 0.10793629404886, 0.10478344432968, </span>
<a name="line-35"></a><span class='hs-comment'>-- > 0.09562326700432, 0.08131651217682, 0.06318761339784 ])</span>
<a name="line-36"></a><span class='hs-comment'>-- </span>
<a name="line-37"></a>
<a name="line-38"></a><a name="fir"></a><span class='hs-definition'>fir</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Fractional</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>ProcType</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-39"></a> <span class='hs-conid'>ProcId</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Signal</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Signal</span> <span class='hs-varid'>b</span>
<a name="line-40"></a><span class='hs-definition'>fir</span> <span class='hs-varid'>id</span> <span class='hs-varid'>h</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>innerProd</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span> <span class='hs-varop'>++</span> <span class='hs-str'>"_innerProd"</span><span class='hs-layout'>)</span> <span class='hs-varid'>h</span> <span class='hs-varop'>.</span> <span class='hs-varid'>sipo</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span> <span class='hs-varop'>++</span> <span class='hs-str'>"_sipo"</span><span class='hs-layout'>)</span> <span class='hs-varid'>k</span> <span class='hs-num'>0.0</span>
<a name="line-41"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span><span class='hs-varop'>.</span><span class='hs-varid'>lengthT</span> <span class='hs-varid'>h</span>
<a name="line-42"></a>
<a name="line-43"></a><a name="sipo"></a><span class='hs-definition'>sipo</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Fractional</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>ProcType</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-44"></a> <span class='hs-conid'>ProcId</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Signal</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-conid'>Signal</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-45"></a><span class='hs-definition'>sipo</span> <span class='hs-varid'>id</span> <span class='hs-varid'>n</span> <span class='hs-varid'>s0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unzipxSY</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span> <span class='hs-varop'>++</span> <span class='hs-str'>"_unzipxSY"</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>scanldSY</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span> <span class='hs-varop'>++</span> <span class='hs-str'>"_scanldSY"</span><span class='hs-layout'>)</span> <span class='hs-varid'>srV</span> <span class='hs-varid'>initState</span>
<a name="line-46"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>initState</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span><span class='hs-varop'>.</span><span class='hs-varid'>copy</span> <span class='hs-varid'>n</span> <span class='hs-varid'>s0</span>
<a name="line-47"></a> <span class='hs-varid'>srV</span> <span class='hs-keyglyph'>=</span> <span class='hs-varop'>$</span><span class='hs-layout'>(</span><span class='hs-varid'>newProcFun</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>d</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>srV</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-48"></a> <span class='hs-varid'>srV</span> <span class='hs-varid'>v</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span><span class='hs-varop'>.</span><span class='hs-varid'>shiftr</span> <span class='hs-varid'>v</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-49"></a>
<a name="line-50"></a><a name="innerProd"></a><span class='hs-definition'>innerProd</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Fractional</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>ProcType</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-51"></a> <span class='hs-conid'>ProcId</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-conid'>Signal</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Signal</span> <span class='hs-varid'>a</span>
<a name="line-52"></a><span class='hs-definition'>innerProd</span> <span class='hs-varid'>id</span> <span class='hs-varid'>h</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>zipWithxSY</span> <span class='hs-varid'>id</span> <span class='hs-layout'>(</span><span class='hs-varid'>ipV</span> <span class='hs-varop'>`defArgVal`</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span>
<a name="line-53"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>ipV</span> <span class='hs-keyglyph'>=</span> <span class='hs-varop'>$</span><span class='hs-layout'>(</span><span class='hs-varid'>newProcFun</span>
<a name="line-54"></a> <span class='hs-comment'>-- We could make the inner product in one traverse </span>
<a name="line-55"></a> <span class='hs-comment'>-- but FSVecs don't allow recursive calls</span>
<a name="line-56"></a> <span class='hs-comment'>-- (they don't allow to check the constraints statically)</span>
<a name="line-57"></a> <span class='hs-comment'>-- Thus, we traverse the vector twice</span>
<a name="line-58"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>d</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>ipV</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-59"></a> <span class='hs-varid'>ipV</span> <span class='hs-varid'>v1</span> <span class='hs-varid'>v2</span> <span class='hs-keyglyph'>=</span>
<a name="line-60"></a> <span class='hs-conid'>V</span><span class='hs-varop'>.</span><span class='hs-varid'>foldl</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <span class='hs-varop'>$</span> <span class='hs-conid'>V</span><span class='hs-varop'>.</span><span class='hs-varid'>zipWith</span> <span class='hs-layout'>(</span><span class='hs-varop'>*</span><span class='hs-layout'>)</span> <span class='hs-varid'>v1</span> <span class='hs-varid'>v2</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
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