dft_decomposition.abw

fft代码,采用蝶形算法,包括C,matlab和verilog代码

<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">Table X summarises the additive terms in the exponent.</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">{ Insert table of terms here}</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">An analysis of these terms yields some simplications.</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">Consider the red area, where p + q &gt; A  -&gt; p&gt;A-q  -&gt;  p-1&gt;A-q.  Here</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal"> nterm(p).kterm(q) = {expression for terms with }</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">Hence e^2pi.{expression}/N = e^2pi.n = 1, since the exponent is n.2pi</c></p>
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<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">These unity terms can be canceled without affecting the value of the DFT.</c></p>
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<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">Consider the green area, where p + q = A  -&gt;  q=A-p.  Here</c></p>
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<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal"> nterm(p).kterm(q) = {expression for terms with }</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">Hence e^2pi.{expression}/N = e^2pi.n = 1, since the exponent is n.2pi</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">These unity terms can be cancelled without affecting the value of the DFT.</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">Consider the blue area, where p + q = A-1  -&gt;  q=A-1-p.  Here</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal"> nterm(p).kterm(q) = {expression for terms with }/Np</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">Hence e^2pi.{expression}/N = e^2pi.n/Np = 1, since the exponent is n.2pi</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">These A terms yield A DFTs, each corresponding to a factor of N.</c></p>
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<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">Consider the yellow area, where p + q &lt; A-1.  Here</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal"> nterm(p).kterm(q) = {expression for terms non-integer term}</c></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"></p>
<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">These terms do not cancel.  They result in multiplying factors between the DFTs corresponding to the &#x2018;blue&#x2019; factors.</c></p>
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<p props="line-height:1.000000; margin-bottom:0.0000in; margin-left:0.0000in; margin-right:0.0000in; margin-top:0.0000in; text-align:left; text-indent:0.0000in"><c props="color:000000; font-family:Times New Roman; font-size:12pt; font-style:normal; font-weight:normal; text-decoration:none; text-position:normal">APPENDIX A: Some example decompositions to allow the reader to spot the pattern</c></p>
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</section>
</abiword>