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<h2>
<span class="refentrytitle">zfilter2</span>
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<p>zfilter2 —
Performs filtering using a transposed form-II digital filter lattice with radial pole-shearing and angular pole-warping.
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<div class="refsect1" title="Description">
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<h2>Description</h2>
<p>
General purpose custom filter with time-varying pole control. The filter coefficients implement the following difference equation:
</p>
<div class="literallayout">
<p><br />
(1)*y(n) = b0*x[n] + b1*x[n-1] +...+ bM*x[n-M] - a1*y[n-1] -...- aN*y[n-N]<br />
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<p>
the system function for which is represented by:
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<p><br />
B(Z) b0 + b1*Z<sup>-1</sup> + ... + bM*Z<sup>-M</sup><br />
H(Z) = ---- = --------------------------<br />
A(Z) 1 + a1*Z<sup>-1</sup> + ... + aN*Z<sup>-N</sup><br />
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<div class="refsect1" title="Syntax">
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<h2>Syntax</h2>
<pre class="synopsis">ares <span class="command"><strong>zfilter2</strong></span> asig, kdamp, kfreq, iM, iN, ib0, ib1, ..., ibM, \
ia1,ia2, ..., iaN</pre>
</div>
<div class="refsect1" title="Initialization">
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<h2>Initialization</h2>
<p>
At initialization the number of zeros and poles of the filter are specified along with the corresponding zero and pole coefficients. The coefficients must be obtained by an external filter-design application such as Matlab and specified directly or loaded into a table via <a class="link" href="GEN01.html" title="GEN01"><em class="citetitle">GEN01</em></a>. With <span class="emphasis"><em>zfilter2</em></span>, the roots of the characteristic polynomials are solved at initialization so that the pole-control operations can be implemented efficiently.
</p>
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<div class="refsect1" title="Performance">
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<h2>Performance</h2>
<p>
The <a class="link" href="filter2.html" title="filter2"><em class="citetitle">filter2</em></a> opcodes perform filtering using a transposed form-II digital filter lattice with no time-varying control. <span class="emphasis"><em>zfilter2</em></span> uses the additional operations of radial pole-shearing and angular pole-warping in the Z plane.
</p>
<p>
Pole shearing increases the magnitude of poles along radial lines in the Z-plane. This has the affect of altering filter ring times. The k-rate variable <span class="emphasis"><em>kdamp</em></span> is the damping parameter. Positive values (0.01 to 0.99) increase the ring-time of the filter (hi-Q), negative values (-0.01 to -0.99) decrease the ring-time of the filter, (lo-Q).
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<p>
Pole warping changes the frequency of poles by moving them along angular paths in the Z plane. This operation leaves the shape of the magnitude response unchanged but alters the frequencies by a constant factor (preserving 0 and p). The k-rate variable <span class="emphasis"><em>kfreq</em></span> determines the frequency warp factor. Positive values (0.01 to 0.99) increase frequencies toward p and negative values (-0.01 to -0.99) decrease frequencies toward 0.
</p>
<p>
Since <span class="emphasis"><em>filter2</em></span> implements generalized recursive filters, it can be used to specify a large range of general DSP algorithms. For example, a digital waveguide can be implemented for musical instrument modeling using a pair of <a class="link" href="delayr.html" title="delayr"><em class="citetitle">delayr</em></a> and <a class="link" href="delayw.html" title="delayw"><em class="citetitle">delayw</em></a> opcodes in conjunction with the <span class="emphasis"><em>filter2</em></span> opcode.
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<div class="refsect1" title="Examples">
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<h2>Examples</h2>
<p>
A controllable second-order IIR filter operating on an a-rate signal:
</p>
<div class="informalexample">
<pre class="programlisting">
a1 <span class="opc">zfilter2</span> asig, kdamp, kfreq, 1, 2, 1, ia1, ia2 <span class="comment">;; controllable a-rate IIR filter</span></pre>
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<p>
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<div class="refsect1" title="See Also">
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<h2>See Also</h2>
<p>
<a class="link" href="filter2.html" title="filter2"><em class="citetitle">filter2</em></a>
</p>
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<div class="refsect1" title="Credits">
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<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
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<td>Author: Michael A. Casey</td>
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<td>M.I.T.</td>
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<td>Cambridge, Mass.</td>
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<td>1997</td>
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<p>New in Version 3.47</p>
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