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<table width="100%" summary="page for fastkernel {Rwave}"><tr><td>fastkernel {Rwave}</td><td align="right">R Documentation</td></tr></table>
<h2>Kernel for Reconstruction from Wavelet Ridges</h2>


<h3>Description</h3>

<p>
Computes the cost from the sample of points on the estimated ridge
and the matrix used in the reconstruction of the original signal,
using simple trapezoidal rule for integrals.
</p>


<h3>Usage</h3>

<pre>
fastkernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>node</code></td>
<td>
values of the variable b for the nodes of the ridge.
</td></tr>
<tr valign="top"><td><code>phinode</code></td>
<td>
values of the scale variable a for the nodes of the ridge.
</td></tr>
<tr valign="top"><td><code>nvoice</code></td>
<td>
number of scales within 1 octave.
</td></tr>
<tr valign="top"><td><code>x.inc</code></td>
<td>
step unit for the computation of the kernel
</td></tr>
<tr valign="top"><td><code>x.min</code></td>
<td>
minimal value of x for the computation of <i>Q_2</i>.
</td></tr>
<tr valign="top"><td><code>x.max</code></td>
<td>
maximal value of x for the computation of <i>Q_2</i>.
</td></tr>
<tr valign="top"><td><code>w0</code></td>
<td>
central frequency of the wavelet
</td></tr>
<tr valign="top"><td><code>plot</code></td>
<td>
if set to TRUE, displays the modulus of the matrix of <i>Q_2</i>.
</td></tr>
</table>

<h3>Details</h3>

<p>
Uses trapezoidal rule (instead of Romberg's method) to evaluate
the kernel.
</p>


<h3>Value</h3>

<p>
matrix of the <i>Q_2</i> kernel.</p>

<h3>References</h3>

<p>
See discussions in the text of ``Practical Time-Frequency Analysis''.
</p>


<h3>See Also</h3>

<p>
<code><a href="kernel.html">kernel</a></code>, <code><a href="rkernel.html">rkernel</a></code>, <code><a href="gkernel.html">gkernel</a></code>,
<code><a href="zerokernel.html">zerokernel</a></code>.
</p>


<h3>Examples</h3>

<pre>
# The function is currently defined as
function(node, phinode, nvoice, x.inc = 1, x.min = node[1], x.max = node[length(node)], w0 = 2 * pi, plot = F)
{
#########################################################################
#     fastkernel:   
#     -----------
#          Same as kernel, except that the kernel is computed
#            using Riemann sums instead of Romberg integration.
#
#     Input:
#     ------
#      node: values of the variable b for the nodes of the ridge
#      phinode: values of the scale variable a for the nodes of the ridge
#      nvoice: number of scales within 1 octave
#      x.inc: step unit for the computation of the kernel
#      x.min: minimal value of x for the computation of Q2
#      x.max: maximal value of x for the computation of Q2
#      w0: central frequency of the wavelet
#      plot: if set to TRUE, displays the modulus of the matrix of Q2
#
#     Output:
#     -------
#      ker: matrix of the Q2 kernel
#
#########################################################################
        lng &lt;- as.integer((x.max - x.min)/x.inc) + 1
        nbnode &lt;- length(node)
        b.start &lt;- x.min - 50
        b.end &lt;- x.max + 50
        ker.r &lt;- matrix(0, lng, lng)
        ker.i &lt;- matrix(0, lng, lng)
        dim(ker.r) &lt;- c(lng * lng, 1)
        dim(ker.i) &lt;- c(lng * lng, 1)
        phinode &lt;- 2 * 2^(phinode/nvoice)
        z &lt;- .C(fastkernel,
                ker.r = as.double(ker.r),
                ker.i = as.double(ker.i),
                as.integer(x.min),
                as.integer(x.max),
                as.integer(x.inc),
                as.integer(lng),
                as.double(node),
                as.double(phinode),
                as.integer(nbnode),
                as.double(w0),
                as.double(b.start),
                as.double(b.end))
        ker.r &lt;- z$ker.r
        ker.i &lt;- z$ker.i
        dim(ker.r) &lt;- c(lng, lng)
        dim(ker.i) &lt;- c(lng, lng)
        ker &lt;- matrix(0, lng, lng)
        i &lt;- sqrt(as.complex(-1))
        ker &lt;- ker.r + i * ker.i
        if(plot == T) {
                par(mfrow = c(1, 1))
                image(Mod(ker))
                title("Matrix of the reconstructing kernel (modulus)")
        }
        ker
}</pre>



<hr><div align="center">[Package <em>Rwave</em> version 1.24 <a href="00Index.html">Index]</a></div>

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