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<section id="multi-rate-synthesis-py-doing-synthesis-at-very-high-sampling-rate">
<h1>01-multi-rate-synthesis.py - Doing synthesis at very high sampling rate.<a class="headerlink" href="#multi-rate-synthesis-py-doing-synthesis-at-very-high-sampling-rate" title="Permalink to this heading">¶</a></h1>
<p>In numerical audio computing, it is sometimes useful to be able to process
a signal with much more timing precision than what the usual sampling rates
offer. A typical case is when the synthesis algorithm generates aliasing in
the output signal. The solution is to increase the sampling rate, so the
nyquist frequency, and to use anti-aliasing filters when converting from one
rate to another.</p>
<p>Pyo allows to compute chunks of code at different sampling rates than the
one with which the server was started. You should do this only for the objects
you need to process with a higher sampling rate, without changing the server’s
sampling rate, otherwise the program will be very CPU consuming.</p>
<p>You start a new resampling block with the method:</p>
<blockquote>
<div><p>Server.beginResamplingBlock(x)</p>
</div></blockquote>
<p>where <cite>x</cite>, a power-of-two, is the resampling factor. A negative power-of-two
will start a downsampling block of code.</p>
<p>To close the block, simply call:</p>
<blockquote>
<div><p>Server.endResamplingBlock()</p>
</div></blockquote>
<p>Everything between the two calls will be computed with the new sampling rate.</p>
<p>Audio signals must be resampled before used with a different sampling rate.
The Resample object does this. Inside a resampling block, it will convert the
signal to the new sampling rate, and outside the resampling block, it will
convert the signal back to the original sampling rate. Its <cite>mode</cite> argument lets
choose the quality of the interpolation/decimation filter used to resample the
signal.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <a class="sphinx-codeautolink-a" href="../../api/alphabetical.html#module-pyo" title="pyo"><span class="nn">pyo</span></a> <span class="kn">import</span> <span class="o">*</span>
<span class="n">s</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/server.html#pyo.Server" title="pyo.lib.server.Server"><span class="n">Server</span></a><span class="p">()</span><span class="o">.</span><span class="n">boot</span><span class="p">()</span>
<span class="c1"># We create a new class for our upsampled Frequency modulation synthesis. We</span>
<span class="c1"># use only the modulation index as parameter in order to simplify the code.</span>
<span class="k">class</span> <span class="nc">UpSampFM</span><span class="p">:</span>
<span class="sd">"""</span>
<span class="sd"> Frequency modulation synthesis that can be computed a higher sampling rate.</span>
<span class="sd"> :Args:</span>
<span class="sd"> fmindex: float or PyoObject, optional</span>
<span class="sd"> The modulation index of the FM synthesis.</span>
<span class="sd"> upfactor: int (power-of-two), optional</span>
<span class="sd"> Resampling factor.</span>
<span class="sd"> filtmode: int, optional</span>
<span class="sd"> The interpolation/decimation mode. See Resample's man page</span>
<span class="sd"> for details.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">fmindex</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">upfactor</span><span class="o">=</span><span class="mi">8</span><span class="p">,</span> <span class="n">filtmode</span><span class="o">=</span><span class="mi">32</span><span class="p">):</span>
<span class="c1"># Convert the modulation index argument to audio signal.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">fmindex</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/controls.html#pyo.Sig" title="pyo.lib._core.Sig"><span class="n">Sig</span></a><span class="p">(</span><span class="n">fmindex</span><span class="p">)</span>
<span class="c1"># Get a reference to the audio server.</span>
<span class="n">server</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">fmindex</span><span class="o">.</span><span class="n">getServer</span><span class="p">()</span>
<span class="c1"># Start an upsampled block of code.</span>
<span class="n">server</span><span class="o">.</span><span class="n">beginResamplingBlock</span><span class="p">(</span><span class="n">upfactor</span><span class="p">)</span>
<span class="c1"># Resample the audio signals. Because the drive signal is only a</span>
<span class="c1"># control signal, a linear interpolation is enough.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">fmindexUp</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/utils.html#pyo.Resample" title="pyo.lib.utils.Resample"><span class="n">Resample</span></a><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fmindex</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="c1"># Generate the FM synthesis.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">fmUp</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.FM" title="pyo.lib.generators.FM"><span class="n">FM</span></a><span class="p">(</span><span class="n">carrier</span><span class="o">=</span><span class="mi">492</span><span class="p">,</span> <span class="n">ratio</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">fmindexUp</span><span class="p">)</span>
<span class="c1"># Close the upsampled block.</span>
<span class="n">server</span><span class="o">.</span><span class="n">endResamplingBlock</span><span class="p">()</span>
<span class="c1"># Convert back the synthesized signal to the current sampling rate.</span>
<span class="c1"># We use a good decimination filter to eliminate aliasing.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">output</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/utils.html#pyo.Resample" title="pyo.lib.utils.Resample"><span class="n">Resample</span></a><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fmUp</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="n">filtmode</span><span class="p">)</span>
<span class="c1"># Define some useful methods.</span>
<span class="k">def</span> <span class="nf">out</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">output</span><span class="o">.</span><span class="n">out</span><span class="p">()</span>
<span class="k">return</span> <span class="bp">self</span>
<span class="k">def</span> <span class="nf">sig</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">output</span>
<span class="c1"># Control for the modulation index parameter of the synthesis.</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/controls.html#pyo.Sig" title="pyo.lib._core.Sig"><span class="n">index</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/controls.html#pyo.Sig" title="pyo.lib._core.Sig"><span class="n">Sig</span></a><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
<span class="n">index</span><span class="o">.</span><span class="n">ctrl</span><span class="p">([</span><a class="sphinx-codeautolink-a" href="../../api/classes/map.html#pyo.SLMap" title="pyo.lib._maps.SLMap"><span class="n">SLMap</span></a><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="s2">"lin"</span><span class="p">,</span> <span class="s2">"value"</span><span class="p">,</span> <span class="mi">20</span><span class="p">)],</span> <span class="n">title</span><span class="o">=</span><span class="s2">"Modulation Index"</span><span class="p">)</span>
<span class="c1"># FM synthesis at current sampling rate.</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.FM" title="pyo.lib.generators.FM"><span class="n">fm1</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.FM" title="pyo.lib.generators.FM"><span class="n">FM</span></a><span class="p">(</span><span class="n">carrier</span><span class="o">=</span><span class="mi">492</span><span class="p">,</span> <span class="n">ratio</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../../api/classes/controls.html#pyo.Sig" title="pyo.lib._core.Sig"><span class="n">index</span></a><span class="p">)</span>
<span class="c1"># FM synthesis with increased sampling rate.</span>
<span class="n">fm2</span> <span class="o">=</span> <span class="n">UpSampFM</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../../api/classes/controls.html#pyo.Sig" title="pyo.lib._core.Sig"><span class="n">index</span></a><span class="p">)</span>
<span class="c1"># Interpolator to compare the two processes.</span>
<span class="n">output</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/utils.html#pyo.Interp" title="pyo.lib.utils.Interp"><span class="n">Interp</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.FM" title="pyo.lib.generators.FM"><span class="n">fm1</span></a><span class="p">,</span> <span class="n">fm2</span><span class="o">.</span><span class="n">sig</span><span class="p">(),</span> <span class="mi">0</span><span class="p">,</span> <span class="n">mul</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span><span class="o">.</span><span class="n">out</span><span class="p">()</span>
<span class="n">output</span><span class="o">.</span><span class="n">ctrl</span><span class="p">([</span><a class="sphinx-codeautolink-a" href="../../api/classes/map.html#pyo.SLMap" title="pyo.lib._maps.SLMap"><span class="n">SLMap</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"lin"</span><span class="p">,</span> <span class="s2">"interp"</span><span class="p">,</span> <span class="mi">0</span><span class="p">)],</span> <span class="n">title</span><span class="o">=</span><span class="s2">"Up Sampling: without <=> with"</span><span class="p">)</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/analysis.html#pyo.Spectrum" title="pyo.lib.analysis.Spectrum"><span class="n">sp</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/analysis.html#pyo.Spectrum" title="pyo.lib.analysis.Spectrum"><span class="n">Spectrum</span></a><span class="p">(</span><span class="n">output</span><span class="p">)</span>
<span class="n">s</span><span class="o">.</span><span class="n">gui</span><span class="p">(</span><span class="nb">locals</span><span class="p">())</span>
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