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<pre style="font-family:Courier New;font-style:normal;font-size:13.0;"><span style="color:rgb(0,0,0);"></span>Hi Scilab users,
<span style="color:rgb(0,0,0);">I</span> <span style="color:rgb(0,0,0);">want</span> <span style="color:rgb(0,0,0);">to</span> <span style="color:rgb(0,0,0);">analyse</span> <span style="color:rgb(0,0,0);">a</span> <span style="color:rgb(0,0,0);">microphone</span> <span style="color:rgb(0,0,0);">recording</span> <span style="color:rgb(0,0,0);">of</span> <span style="color:rgb(0,0,0);">the</span> <span style="color:rgb(174,92,176);text-decoration:underline;">sound</span> <span style="color:rgb(188,143,143);">of</span> <span style="color:rgb(188,143,143);">a</span> <span style="color:rgb(188,143,143);">bell</span> <span style="color:rgb(188,143,143);">or</span> <span style="color:rgb(188,143,143);">gong. </span><span style="color:rgb(0,0,0);">Given</span> <span style="color:rgb(0,0,0);">ia</span> <span style="color:rgb(0,0,0);">the</span> <span style="color:rgb(0,0,0);">equidistantly</span> <span style="color:rgb(0,0,0);">sampled</span> <span style="color:rgb(174,92,176);text-decorati
on:underline;">sound</span> <span style="color:rgb(188,143,143);">pressure</span> <span style="color:rgb(188,143,143);">y(t)</span> <span style="color:rgb(188,143,143);">after</span> <span style="color:rgb(188,143,143);">a</span> <span style="color:rgb(188,143,143);">stroke</span> <span style="color:rgb(188,143,143);">for</span> <span style="color:rgb(188,143,143);">10</span> <span style="color:rgb(188,143,143);">s</span>.
<span style="color:rgb(0,0,0);">The</span> <span style="color:rgb(0,0,0);">ansatz</span>
<span style="color:rgb(0,0,0);">y</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(50,185,185);">sum</span><span style="color:rgb(74,85,219);">(</span> <span style="color:rgb(0,0,0);">A_i</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(50,185,185);">exp</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">d_i</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(0,0,0);">t</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(50,185,185);">cos</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(218,112,214);">%pi</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(0,0,0);">f_i</span><span style="color:rgb(92,92,92);
">+</span><span style="color:rgb(0,0,0);">alpha_i</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(74,85,219);">)</span> for i=1,2,...5 or more
<span style="color:rgb(0,0,0);">is</span> <span style="color:rgb(0,0,0);">assumed</span> <span style="color:rgb(0,0,0);">to</span> <span style="color:rgb(0,0,0);">approximate</span> <span style="color:rgb(0,0,0);">the</span> <span style="color:rgb(0,0,0);">signal</span> <span style="color:rgb(50,185,185);">where</span> <span style="color:rgb(188,143,143);">A_i</span><span style="color:rgb(0,0,0);">,</span> <span style="color:rgb(0,0,0);">d_i</span><span style="color:rgb(0,0,0);">,</span> <span style="color:rgb(0,0,0);">f_i</span><span style="color:rgb(0,0,0);">,</span> <span style="color:rgb(50,185,185);">and</span> <span style="color:rgb(188,143,143);">alpha_i</span> <span style="color:rgb(188,143,143);">are</span> <span style="color:rgb(188,143,143);">the</span> <span style="color:rgb(188,143,143);">unknown</span> <span style="color:rgb(188,143,143);">amplitudes</span><span style="color:rgb(0,0,0);">,</span> <span style="color:rgb(0,0,0);">danping</span> <span style="color:rgb(174
,92,176);text-decoration:underline;">factors</span><span style="color:rgb(0,0,0);">,</span> <span style="color:rgb(0,0,0);">frequencies</span><span style="color:rgb(0,0,0);">,</span> <span style="color:rgb(50,185,185);">and</span> <span style="color:rgb(188,143,143);">phase</span> <span style="color:rgb(188,143,143);">angles</span> <span style="color:rgb(188,143,143);">of</span> <span style="color:rgb(188,143,143);">y.</span> <span style="color:rgb(188,143,143);">The</span> <span style="color:rgb(188,143,143);">analysis</span> <span style="color:rgb(188,143,143);">may</span> <span style="color:rgb(188,143,143);">be</span> <span style="color:rgb(188,143,143);">restricted</span> <span style="color:rgb(188,143,143);">to</span> <span style="color:rgb(188,143,143);">the</span> <span style="color:rgb(188,143,143);">lowest</span> <span style="color:rgb(188,143,143);">5</span> <span style="color:rgb(188,143,143);">frequencies</span> <span style="color:rgb(188,143,143);">fi.</span>
<span style="color:rgb(0,0,0);">Does</span> <span style="color:rgb(0,0,0);">Scilab</span> <span style="color:rgb(0,0,0);">offer</span> <span style="color:rgb(0,0,0);">a</span> <span style="color:rgb(0,0,0);">method</span> <span style="color:rgb(160,32,240);">for</span> <span style="color:rgb(0,0,0);">this?</span> <span style="color:rgb(0,0,0);">FFT seems not to be adequate</span><span style="color:rgb(0,0,0);"></span> <span style="color:rgb(0,0,0);">because</span> <span style="color:rgb(0,0,0);">the</span> <span style="color:rgb(0,0,0);">signal</span> <span style="color:rgb(0,0,0);">is</span> <span style="color:rgb(0,0,0);">aperiodic</span> <span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">silence</span> <span style="color:rgb(0,0,0);">after</span> <span style="color:rgb(188,143,143);">10</span> <span style="color:rgb(0,0,0);">s</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">.</span>
<span style="color:rgb(0,0,0);">Is</span> <span style="color:rgb(0,0,0);">nonlinear</span> <span style="color:rgb(0,0,0);">regression</span> <span style="color:rgb(74,85,219);">(with which </span><span style="color:rgb(0,0,0);">I</span><span style="color:rgb(92,92,92);">'</span><span style="color:rgb(0,0,0);">m</span> <span style="color:rgb(0,0,0);">fmiliar</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(0,0,0);">a</span> <span style="color:rgb(0,0,0);">promising</span> <span style="color:rgb(0,0,0);">way</span><span style="color:rgb(92,92,92);">.</span> <span style="color:rgb(0,0,0);">The</span> <span style="color:rgb(0,0,0);">lowest</span> <span style="color:rgb(0,0,0);">frequencies</span> <span style="color:rgb(0,0,0);">can</span> <span style="color:rgb(0,0,0);">probably</span> <span style="color:rgb(0,0,0);">be</span> <span style="color:rgb(0,0,0);">concluded</span> <span style="color:rgb(0,0,0);">from</span> <span style="color:rgb(0,0,0);">a</span> <sp
an style="color:rgb(0,0,0);">short</span> <span style="color:rgb(0,0,0);">time</span> <span style="color:rgb(0,0,0);">DFT</span> <span style="color:rgb(50,185,185);">where</span> <span style="color:rgb(188,143,143);">damping</span> <span style="color:rgb(188,143,143);">is</span> <span style="color:rgb(188,143,143);">negligible.
Kind regards
Jens
</span></pre>
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