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<h2>
<span class="refentrytitle">biquad</span>
</h2>
<p>biquad —
A sweepable general purpose biquadratic digital filter.
</p>
</div>
<div class="refsect1" title="Description">
<a id="idp14808864"></a>
<h2>Description</h2>
<p>
A sweepable general purpose biquadratic digital filter.
</p>
</div>
<div class="refsect1" title="Syntax">
<a id="idp14848256"></a>
<h2>Syntax</h2>
<pre class="synopsis">ares <span class="command"><strong>biquad</strong></span> asig, kb0, kb1, kb2, ka0, ka1, ka2 [, iskip]</pre>
</div>
<div class="refsect1" title="Initialization">
<a id="idp14849384"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>iskip</em></span> (optional, default=0) -- if non-zero, intialization will be skipped. Default value 0. (New in Csound version 3.50)
</p>
</div>
<div class="refsect1" title="Performance">
<a id="idp14850456"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>asig</em></span> -- input signal
</p>
<p>
<span class="emphasis"><em>biquad</em></span> is a general purpose biquadratic digital filter of the form:
</p>
<div class="literallayout">
<p><br />
a0*y(n) + a1*y[n-1] + a2*y[n-2] = b0*x[n] + b1*x[n-1] + b2*x[n-2]<br />
</p>
</div>
<p>
</p>
<p>
This filter has the following frequency response:
</p>
<div class="literallayout">
<p><br />
B(Z) b0 + b1*Z<sup>-1</sup> + b2*Z<sup>-2</sup><br />
H(Z) = ---- = ------------------<br />
A(Z) a0 + a1*Z<sup>-1</sup> + a2*Z<sup>-2</sup><br />
</p>
</div>
<p>
</p>
<p>
This type of filter is often encountered in digital signal processing literature. It allows six user-defined k-rate coefficients.
</p>
</div>
<div class="refsect1" title="Examples">
<a id="idp14854832"></a>
<h2>Examples</h2>
<p>
Here is an example of the biquad opcode. It uses the file <a class="ulink" href="examples/biquad.csd" target="_top"><em class="citetitle">biquad.csd</em></a>.
</p>
<div class="example">
<a id="idp14855808"></a>
<p class="title">
<strong>Example 81. Example of the biquad opcode.</strong>
</p>
<div class="example-contents">
<p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
<pre class="programlisting">
<span class="csdtag"><CsoundSynthesizer></span>
<span class="csdtag"><CsOptions></span>
<span class="comment">; Select audio/midi flags here according to platform</span>
<span class="comment">; Audio out Audio in No messages</span>
-odac -iadc -d <span class="comment">;;;RT audio I/O</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o biquad.wav -W ;;; for file output any platform</span>
<span class="csdtag"></CsOptions></span>
<span class="csdtag"><CsInstruments></span>
<span class="comment">; Initialize the global variables.</span>
<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">kr</span> <span class="op">=</span> 4410
<span class="ohdr">ksmps</span> <span class="op">=</span> 10
<span class="ohdr">nchnls</span> <span class="op">=</span> 2
<span class="comment">; Instrument #1.</span>
<span class="oblock">instr</span> 1
<span class="comment">; Get the values from the score.</span>
idur <span class="op">=</span> p3
iamp <span class="op">=</span> p4
icps <span class="op">=</span> <span class="opc">cpspch</span>(p5)
kfco <span class="op">=</span> p6
krez <span class="op">=</span> p7
<span class="comment">; Calculate the biquadratic filter's coefficients </span>
kfcon <span class="op">=</span> 2<span class="op">*</span>3.14159265<span class="op">*</span>kfco<span class="op">/</span><span class="ohdr">sr</span>
kalpha <span class="op">=</span> 1<span class="op">-</span>2<span class="op">*</span>krez<span class="op">*</span><span class="opc">cos</span>(kfcon)<span class="op">*</span><span class="opc">cos</span>(kfcon)<span class="op">+</span>krez<span class="op">*</span>krez<span class="op">*</span><span class="opc">cos</span>(2<span class="op">*</span>kfcon)
kbeta <span class="op">=</span> krez<span class="op">*</span>krez<span class="op">*</span><span class="opc">sin</span>(2<span class="op">*</span>kfcon)<span class="op">-</span>2<span class="op">*</span>krez<span class="op">*</span><span class="opc">cos</span>(kfcon)<span class="op">*</span><span class="opc">sin</span>(kfcon)
kgama <span class="op">=</span> 1<span class="op">+</span><span class="opc">cos</span>(kfcon)
km1 <span class="op">=</span> kalpha<span class="op">*</span>kgama<span class="op">+</span>kbeta<span class="op">*</span><span class="opc">sin</span>(kfcon)
km2 <span class="op">=</span> kalpha<span class="op">*</span>kgama<span class="op">-</span>kbeta<span class="op">*</span><span class="opc">sin</span>(kfcon)
kden <span class="op">=</span> <span class="opc">sqrt</span>(km1<span class="op">*</span>km1<span class="op">+</span>km2<span class="op">*</span>km2)
kb0 <span class="op">=</span> 1.5<span class="op">*</span>(kalpha<span class="op">*</span>kalpha<span class="op">+</span>kbeta<span class="op">*</span>kbeta)<span class="op">/</span>kden
kb1 <span class="op">=</span> kb0
kb2 <span class="op">=</span> 0
ka0 <span class="op">=</span> 1
ka1 <span class="op">=</span> <span class="op">-</span>2<span class="op">*</span>krez<span class="op">*</span><span class="opc">cos</span>(kfcon)
ka2 <span class="op">=</span> krez<span class="op">*</span>krez
<span class="comment">; Generate an input signal.</span>
axn <span class="opc">vco</span> 1, icps, 1
<span class="comment">; Filter the input signal.</span>
ayn <span class="opc">biquad</span> axn, kb0, kb1, kb2, ka0, ka1, ka2
<span class="opc">outs</span> ayn<span class="op">*</span>iamp<span class="op">/</span>2, ayn<span class="op">*</span>iamp<span class="op">/</span>2
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="comment">; Table #1, a sine wave.</span>
<span class="stamnt">f</span> 1 0 16384 10 1
<span class="comment">; Sta Dur Amp Pitch Fco Rez</span>
<span class="stamnt">i</span> 1 0.0 1.0 20000 6.00 1000 .8
<span class="stamnt">i</span> 1 1.0 1.0 20000 6.03 2000 .95
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
</div>
</div>
<p><br class="example-break" />
</p>
<p>
Here is another example of the biquad opcode used for modal synthesis. It uses the file <a class="ulink" href="examples/biquad-2.csd" target="_top"><em class="citetitle">biquad-2.csd</em></a>. See the <a class="link" href="MiscModalFreq.html" title="Appendix E. Modal Frequency Ratios"><em class="citetitle">Modal Frequency Ratios</em></a> appendix for other frequency ratios.
</p>
<div class="example">
<a id="idp14859312"></a>
<p class="title">
<strong>Example 82. Example of the biquad opcode for modal synthesis.</strong>
</p>
<div class="example-contents">
<pre class="programlisting">
<span class="csdtag"><CsoundSynthesizer></span>
<span class="csdtag"><CsOptions></span>
<span class="comment">; Select audio/midi flags here according to platform</span>
<span class="comment">; Audio out Audio in</span>
-odac -iadc <span class="comment">;;;RT audio I/O</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o biquad-2.wav -W ;;; for file output any platform</span>
<span class="csdtag"></CsOptions></span>
<span class="csdtag"><CsInstruments></span>
<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">kr</span> <span class="op">=</span> 4410
<span class="ohdr">ksmps</span> <span class="op">=</span> 10
<span class="ohdr">nchnls</span> <span class="op">=</span> 2
<span class="op">/</span><span class="op">*</span> modal synthesis using <span class="opc">biquad</span> filters as oscillators
Example by Scott Lindroth 2007 <span class="op">*</span><span class="op">/</span>
<span class="oblock">instr</span> 1
ipi <span class="op">=</span> 3.1415926
idenom <span class="op">=</span> <span class="ohdr">sr</span><span class="op">*</span>0.5
ipulseSpd <span class="op">=</span> p4
icps <span class="op">=</span> p5
ipan <span class="op">=</span> p6
iamp <span class="op">=</span> p7
iModes <span class="op">=</span> p8
apulse <span class="opc">mpulse</span> iamp, 0
icps <span class="op">=</span> <span class="opc">cpspch</span>( icps )
<span class="comment">; filter gain</span>
iamp1 <span class="op">=</span> 600
iamp2 <span class="op">=</span> 1000
iamp3 <span class="op">=</span> 1000
iamp4 <span class="op">=</span> 1000
iamp5 <span class="op">=</span> 1000
iamp6 <span class="op">=</span> 1000
<span class="comment">; resonance</span>
irpole1 <span class="op">=</span> 0.99999
irpole2 <span class="op">=</span> irpole1
irpole3 <span class="op">=</span> irpole1
irpole4 <span class="op">=</span> irpole1
irpole5 <span class="op">=</span> irpole1
irpole6 <span class="op">=</span> irpole1
<span class="comment">; modal frequencies</span>
<span class="octrl">if</span> (iModes <span class="op">==</span> 1) <span class="octrl">goto</span> modes1
<span class="octrl">if</span> (iModes <span class="op">==</span> 2) <span class="octrl">goto</span> modes2
modes1<span class="op">:</span>
if1 <span class="op">=</span> icps <span class="op">*</span> 1 <span class="comment">;pot lid</span>
if2 <span class="op">=</span> icps <span class="op">*</span> 6.27
if3 <span class="op">=</span> icps <span class="op">*</span> 3.2
if4 <span class="op">=</span> icps <span class="op">*</span> 9.92
if5 <span class="op">=</span> icps <span class="op">*</span> 14.15
if6 <span class="op">=</span> icps <span class="op">*</span> 6.23
<span class="octrl">goto</span> nextPart
modes2<span class="op">:</span>
if1 <span class="op">=</span> icps <span class="op">*</span> 1 <span class="comment">;uniform wood bar</span>
if2 <span class="op">=</span> icps <span class="op">*</span> 2.572
if3 <span class="op">=</span> icps <span class="op">*</span> 4.644
if4 <span class="op">=</span> icps <span class="op">*</span> 6.984
if5 <span class="op">=</span> icps <span class="op">*</span> 9.723
if6 <span class="op">=</span> icps <span class="op">*</span> 12.0
<span class="octrl">goto</span> nextPart
nextPart<span class="op">:</span>
<span class="comment">; convert frequency to radian frequency</span>
itheta1 <span class="op">=</span> (if1<span class="op">/</span>idenom) <span class="op">*</span> ipi
itheta2 <span class="op">=</span> (if2<span class="op">/</span>idenom) <span class="op">*</span> ipi
itheta3 <span class="op">=</span> (if3<span class="op">/</span>idenom) <span class="op">*</span> ipi
itheta4 <span class="op">=</span> (if4<span class="op">/</span>idenom) <span class="op">*</span> ipi
itheta5 <span class="op">=</span> (if5<span class="op">/</span>idenom) <span class="op">*</span> ipi
itheta6 <span class="op">=</span> (if6<span class="op">/</span>idenom) <span class="op">*</span> ipi
<span class="comment">; calculate coefficients</span>
ib11 <span class="op">=</span> <span class="op">-</span>2 <span class="op">*</span> irpole1 <span class="op">*</span> <span class="opc">cos</span>(itheta1)
ib21 <span class="op">=</span> irpole1 <span class="op">*</span> irpole1
ib12 <span class="op">=</span> <span class="op">-</span>2 <span class="op">*</span> irpole2 <span class="op">*</span> <span class="opc">cos</span>(itheta2)
ib22 <span class="op">=</span> irpole2 <span class="op">*</span> irpole2
ib13 <span class="op">=</span> <span class="op">-</span>2 <span class="op">*</span> irpole3 <span class="op">*</span> <span class="opc">cos</span>(itheta3)
ib23 <span class="op">=</span> irpole3 <span class="op">*</span> irpole3
ib14 <span class="op">=</span> <span class="op">-</span>2 <span class="op">*</span> irpole4 <span class="op">*</span> <span class="opc">cos</span>(itheta4)
ib24 <span class="op">=</span> irpole4 <span class="op">*</span> irpole4
ib15 <span class="op">=</span> <span class="op">-</span>2 <span class="op">*</span> irpole5 <span class="op">*</span> <span class="opc">cos</span>(itheta5)
ib25 <span class="op">=</span> irpole5 <span class="op">*</span> irpole5
ib16 <span class="op">=</span> <span class="op">-</span>2 <span class="op">*</span> irpole6 <span class="op">*</span> <span class="opc">cos</span>(itheta6)
ib26 <span class="op">=</span> irpole6 <span class="op">*</span> irpole6
<span class="comment">;printk 1, ib 11</span>
<span class="comment">;printk 1, ib 21</span>
<span class="comment">; also try setting the -1 coeff. to 0, but be sure to scale down the amplitude!</span>
asin1 <span class="opc">biquad</span> apulse <span class="op">*</span> iamp1, 1, 0, <span class="op">-</span>1, 1, ib11, ib21
asin2 <span class="opc">biquad</span> apulse <span class="op">*</span> iamp2, 1, 0, <span class="op">-</span>1, 1, ib12, ib22
asin3 <span class="opc">biquad</span> apulse <span class="op">*</span> iamp3, 1, 0, <span class="op">-</span>1, 1, ib13, ib23
asin4 <span class="opc">biquad</span> apulse <span class="op">*</span> iamp4, 1, 0, <span class="op">-</span>1, 1, ib14, ib24
asin5 <span class="opc">biquad</span> apulse <span class="op">*</span> iamp5, 1, 0, <span class="op">-</span>1, 1, ib15, ib25
asin6 <span class="opc">biquad</span> apulse <span class="op">*</span> iamp6, 1, 0, <span class="op">-</span>1, 1, ib16, ib26
afin <span class="op">=</span> (asin1 <span class="op">+</span> asin2 <span class="op">+</span> asin3 <span class="op">+</span> asin4 <span class="op">+</span> asin5 <span class="op">+</span> asin6)
<span class="opc">outs</span> afin <span class="op">*</span> <span class="opc">sqrt</span>(p6), afin<span class="op">*</span><span class="opc">sqrt</span>(1<span class="op">-</span>p6)
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="comment">;ins st dur pulseSpd pch pan amp Modes</span>
<span class="stamnt">i</span>1 0 12 0 7.089 0 0.7 2
<span class="stamnt">i</span>1 . . . 7.09 1 . .
<span class="stamnt">i</span>1 . . . 7.091 0.5 . .
<span class="stamnt">i</span>1 0 12 0 8.039 0 0.7 2
<span class="stamnt">i</span>1 0 12 0 8.04 1 0.7 2
<span class="stamnt">i</span>1 0 12 0 8.041 0.5 0.7 2
<span class="stamnt">i</span>1 9 . . 7.089 0 . 2
<span class="stamnt">i</span>1 . . . 7.09 1 . .
<span class="stamnt">i</span>1 . . . 7.091 0.5 . .
<span class="stamnt">i</span>1 9 12 0 8.019 0 0.7 2
<span class="stamnt">i</span>1 9 12 0 8.02 1 0.7 2
<span class="stamnt">i</span>1 9 12 0 8.021 0.5 0.7 2
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
</div>
</div>
<p><br class="example-break" />
</p>
</div>
<div class="refsect1" title="See Also">
<a id="idp14860320"></a>
<h2>See Also</h2>
<p>
<a class="link" href="biquada.html" title="biquada"><em class="citetitle">biquada</em></a>,
<a class="link" href="moogvcf.html" title="moogvcf"><em class="citetitle">moogvcf</em></a>,
<a class="link" href="rezzy.html" title="rezzy"><em class="citetitle">rezzy</em></a>
</p>
</div>
<div class="refsect1" title="Credits">
<a id="idp14862344"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Hans Mikelson</td>
</tr>
<tr>
<td>October 1998</td>
</tr>
</table>
<p>
</p>
<p>New in Csound version 3.49</p>
</div>
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