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Discrete Fourier transform: Difference between revisions

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Discrete Fourier transform (view source)

Revision as of 00:27, 28 April 2021

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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">complex</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">complex_new</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)*(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">yk</span> <span style="color: #0000FF;">=</span> <span style="color: #0000007060A8;">complex_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yk</span><span style="color: #0000FF;">,</span><span style="color: #0000007060A8;">complex_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">],</span><span style="color: #0000007060A8;">complex_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">yk</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">complex</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">complex_new</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)*(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">xn</span> <span style="color: #0000FF;">=</span> <span style="color: #0000007060A8;">complex_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xn</span><span style="color: #0000FF;">,</span><span style="color: #0000007060A8;">complex_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #0000007060A8;">complex_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">xn</span> <span style="color: #0000FF;">=</span> <span style="color: #0000007060A8;">complex_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">// clean xn to remove very small imaginary values, and round reals to 14dp</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #0000007060A8;">complex_imag</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xn</span><span style="color: #0000FF;">))<</span><span style="color: #000000;">1e-14</span> <span style="color: #008080;">then</span> <span style="color: #000000;">xn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">round</span><span style="color: #0000FF;">(</span><span style="color: #0000007060A8;">complex_real</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xn</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1e14</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xn</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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