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1 <html>
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2 <head>
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3
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4 <meta charset="UTF-8">
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5
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6 <style type="text/css">
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7 body { margin: 5%; }
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8 table, td, th { border: 0.1em solid #e0e0e0; border-collapse: collapse }
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9 td, th { padding: 0.5em }
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10 </style>
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11
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12 <script src="nayuki/fft.js"></script>
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13 <script src="fft.js/lib/complex.js"></script>
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14 <script src="jsfft/lib/complex_array.js"></script>
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15 <script src="jsfft/lib/fft.js"></script>
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16 <script src="cross/Cross.js"></script>
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17 <script src="cross/FFT.js"></script>
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18 <script src="test.js"></script>
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19
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20 </head>
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21 <body>
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22
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23 <h3>Results</h3>
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24
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25 <p id="test-description"></p>
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26
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27 <table>
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28 <tr>
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29 <th>Implementation</th><th>Result</th><th>Time (first half)</th><th>Time (second half)</th><th>Rate (second half)</th>
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30 </tr>
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31 <tr>
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32 <td>Nayuki</td><td id="nayuki-result"></td><td id="nayuki-1"></td><td id="nayuki-2"></td><td id="nayuki-itr"></td>
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33 </tr><tr>
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34 <td>Nockert</td><td id="nockert-result"></td><td id="nockert-1"></td><td id="nockert-2"></td><td id="nockert-itr"></td>
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35 </tr><tr>
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36 <td>Dntj</td><td id="dntj-result"></td><td id="dntj-1"></td><td id="dntj-2"></td><td id="dntj-itr"></td>
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37 </tr><tr>
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38 <td>Cross</td><td id="cross-result"></td><td id="cross-1"></td><td id="cross-2"></td><td id="cross-itr"></td>
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39 </tr>
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40 </table>
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41
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42 <h3>Notes</h3>
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43
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44 <ul>
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45 <li><b>Nayuki</b>: in-place single-precision complex-complex</li>
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46 <li><b>Nockert</b>: double-precision real-complex</li>
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47 <li><b>Nayuki</b>: double-precision complex-complex. Forward transform is scaled and I've scaled it back again here, which may introduce rounding error.</li>
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48 <li><b>Cross</b>: double-precision real-complex in C, compiled with Emscripten. This is considered a slow implementation amongst native code ones.</li>
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49 </ul>
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50
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51 <h3>Rationale</h3>
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52
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53 <p>If 2150 iterations of real-to-complex FFT of size 2048 takes less
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54 than 10 seconds, then we may be able to make a high quality
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55 real-time phase vocoder (just).</p>
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56
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57 <p>A phase-vocoder of course must use overlapped windowed FFT
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58 (although you can choose the size, within limits), IFFT, and
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59 cartesian-polar conversion to calculate the phase for the
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60 instantaneous frequency.</p>
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61
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62 <p>A reasonable estimate of CPU cost for the whole thing is
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63 somewhere around 10x the cost of simple non-overlapping short-time
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64 forward Fourier transforms across the signal. </p>
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65
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66 <p>2150 iterations corresponds to 100 seconds of audio
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67 non-overlapped at 44.1kHz, so if that takes less than 10 seconds,
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68 then in theory we might be OK.</p>
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69
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70 </body>
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71
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