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8 FastFourierTransformer (Commons Math 2.1 API)
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90 <H2>
91 <FONT SIZE="-1">
92 org.apache.commons.math.transform</FONT>
93 <BR>
94 Class FastFourierTransformer</H2>
95 <PRE>
96 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
97 <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math.transform.FastFourierTransformer</B>
98 </PRE>
99 <DL>
100 <DT><B>All Implemented Interfaces:</B> <DD><A HREF="http://java.sun.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A></DD>
101 </DL>
102 <HR>
103 <DL>
104 <DT><PRE>public class <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.46"><B>FastFourierTransformer</B></A><DT>extends <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="http://java.sun.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A></DL>
105 </PRE>
106
107 <P>
108 Implements the <a href="http://mathworld.wolfram.com/FastFourierTransform.html">
109 Fast Fourier Transform</a> for transformation of one-dimensional data sets.
110 For reference, see <b>Applied Numerical Linear Algebra</b>, ISBN 0898713897,
111 chapter 6.
112 <p>
113 There are several conventions for the definition of FFT and inverse FFT,
114 mainly on different coefficient and exponent. Here the equations are listed
115 in the comments of the corresponding methods.</p>
116 <p>
117 We require the length of data set to be power of 2, this greatly simplifies
118 and speeds up the code. Users can pad the data with zeros to meet this
119 requirement. There are other flavors of FFT, for reference, see S. Winograd,
120 <i>On computing the discrete Fourier transform</i>, Mathematics of Computation,
121 32 (1978), 175 - 199.</p>
122 <P>
123
124 <P>
125 <DL>
126 <DT><B>Since:</B></DT>
127 <DD>1.2</DD>
128 <DT><B>Version:</B></DT>
129 <DD>$Revision: 885278 $ $Date: 2009-11-29 16:47:51 -0500 (Sun, 29 Nov 2009) $</DD>
130 <DT><B>See Also:</B><DD><A HREF="../../../../../serialized-form.html#org.apache.commons.math.transform.FastFourierTransformer">Serialized Form</A></DL>
131 <HR>
132
133 <P>
134
135 <!-- ======== CONSTRUCTOR SUMMARY ======== -->
136
137 <A NAME="constructor_summary"><!-- --></A>
138 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
139 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
140 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
141 <B>Constructor Summary</B></FONT></TH>
142 </TR>
143 <TR BGCOLOR="white" CLASS="TableRowColor">
144 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#FastFourierTransformer()">FastFourierTransformer</A></B>()</CODE>
145
146 <BR>
147 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Construct a default transformer.</TD>
148 </TR>
149 </TABLE>
150 &nbsp;
151 <!-- ========== METHOD SUMMARY =========== -->
152
153 <A NAME="method_summary"><!-- --></A>
154 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
155 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
156 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
157 <B>Method Summary</B></FONT></TH>
158 </TR>
159 <TR BGCOLOR="white" CLASS="TableRowColor">
160 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
161 <CODE>protected &nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
162 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#fft(org.apache.commons.math.complex.Complex[])">fft</A></B>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;data)</CODE>
163
164 <BR>
165 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).</TD>
166 </TR>
167 <TR BGCOLOR="white" CLASS="TableRowColor">
168 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
169 <CODE>protected &nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
170 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#fft(double[], boolean)">fft</A></B>(double[]&nbsp;f,
171 boolean&nbsp;isInverse)</CODE>
172
173 <BR>
174 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).</TD>
175 </TR>
176 <TR BGCOLOR="white" CLASS="TableRowColor">
177 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
178 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
179 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#inversetransform(org.apache.commons.math.complex.Complex[])">inversetransform</A></B>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f)</CODE>
180
181 <BR>
182 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Inversely transform the given complex data set.</TD>
183 </TR>
184 <TR BGCOLOR="white" CLASS="TableRowColor">
185 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
186 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
187 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#inversetransform(double[])">inversetransform</A></B>(double[]&nbsp;f)</CODE>
188
189 <BR>
190 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Inversely transform the given real data set.</TD>
191 </TR>
192 <TR BGCOLOR="white" CLASS="TableRowColor">
193 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
194 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
195 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#inversetransform(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)">inversetransform</A></B>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
196 double&nbsp;min,
197 double&nbsp;max,
198 int&nbsp;n)</CODE>
199
200 <BR>
201 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Inversely transform the given real function, sampled on the given interval.</TD>
202 </TR>
203 <TR BGCOLOR="white" CLASS="TableRowColor">
204 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
205 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
206 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#inversetransform2(org.apache.commons.math.complex.Complex[])">inversetransform2</A></B>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f)</CODE>
207
208 <BR>
209 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Inversely transform the given complex data set.</TD>
210 </TR>
211 <TR BGCOLOR="white" CLASS="TableRowColor">
212 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
213 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
214 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#inversetransform2(double[])">inversetransform2</A></B>(double[]&nbsp;f)</CODE>
215
216 <BR>
217 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Inversely transform the given real data set.</TD>
218 </TR>
219 <TR BGCOLOR="white" CLASS="TableRowColor">
220 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
221 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
222 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#inversetransform2(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)">inversetransform2</A></B>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
223 double&nbsp;min,
224 double&nbsp;max,
225 int&nbsp;n)</CODE>
226
227 <BR>
228 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Inversely transform the given real function, sampled on the given interval.</TD>
229 </TR>
230 <TR BGCOLOR="white" CLASS="TableRowColor">
231 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
232 <CODE>static&nbsp;boolean</CODE></FONT></TD>
233 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#isPowerOf2(long)">isPowerOf2</A></B>(long&nbsp;n)</CODE>
234
235 <BR>
236 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns true if the argument is power of 2.</TD>
237 </TR>
238 <TR BGCOLOR="white" CLASS="TableRowColor">
239 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
240 <CODE>&nbsp;<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></CODE></FONT></TD>
241 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#mdfft(java.lang.Object, boolean)">mdfft</A></B>(<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>&nbsp;mdca,
242 boolean&nbsp;forward)</CODE>
243
244 <BR>
245 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Performs a multi-dimensional Fourier transform on a given array.</TD>
246 </TR>
247 <TR BGCOLOR="white" CLASS="TableRowColor">
248 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
249 <CODE>static&nbsp;double[]</CODE></FONT></TD>
250 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#sample(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)">sample</A></B>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
251 double&nbsp;min,
252 double&nbsp;max,
253 int&nbsp;n)</CODE>
254
255 <BR>
256 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Sample the given univariate real function on the given interval.</TD>
257 </TR>
258 <TR BGCOLOR="white" CLASS="TableRowColor">
259 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
260 <CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
261 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#scaleArray(org.apache.commons.math.complex.Complex[], double)">scaleArray</A></B>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f,
262 double&nbsp;d)</CODE>
263
264 <BR>
265 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Multiply every component in the given complex array by the
266 given real number.</TD>
267 </TR>
268 <TR BGCOLOR="white" CLASS="TableRowColor">
269 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
270 <CODE>static&nbsp;double[]</CODE></FONT></TD>
271 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#scaleArray(double[], double)">scaleArray</A></B>(double[]&nbsp;f,
272 double&nbsp;d)</CODE>
273
274 <BR>
275 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Multiply every component in the given real array by the
276 given real number.</TD>
277 </TR>
278 <TR BGCOLOR="white" CLASS="TableRowColor">
279 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
280 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
281 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#transform(org.apache.commons.math.complex.Complex[])">transform</A></B>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f)</CODE>
282
283 <BR>
284 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform the given complex data set.</TD>
285 </TR>
286 <TR BGCOLOR="white" CLASS="TableRowColor">
287 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
288 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
289 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#transform(double[])">transform</A></B>(double[]&nbsp;f)</CODE>
290
291 <BR>
292 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform the given real data set.</TD>
293 </TR>
294 <TR BGCOLOR="white" CLASS="TableRowColor">
295 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
296 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
297 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#transform(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)">transform</A></B>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
298 double&nbsp;min,
299 double&nbsp;max,
300 int&nbsp;n)</CODE>
301
302 <BR>
303 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform the given real function, sampled on the given interval.</TD>
304 </TR>
305 <TR BGCOLOR="white" CLASS="TableRowColor">
306 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
307 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
308 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#transform2(org.apache.commons.math.complex.Complex[])">transform2</A></B>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f)</CODE>
309
310 <BR>
311 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform the given complex data set.</TD>
312 </TR>
313 <TR BGCOLOR="white" CLASS="TableRowColor">
314 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
315 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
316 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#transform2(double[])">transform2</A></B>(double[]&nbsp;f)</CODE>
317
318 <BR>
319 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform the given real data set.</TD>
320 </TR>
321 <TR BGCOLOR="white" CLASS="TableRowColor">
322 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
323 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]</CODE></FONT></TD>
324 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#transform2(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)">transform2</A></B>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
325 double&nbsp;min,
326 double&nbsp;max,
327 int&nbsp;n)</CODE>
328
329 <BR>
330 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform the given real function, sampled on the given interval.</TD>
331 </TR>
332 <TR BGCOLOR="white" CLASS="TableRowColor">
333 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
334 <CODE>static&nbsp;void</CODE></FONT></TD>
335 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#verifyDataSet(double[])">verifyDataSet</A></B>(double[]&nbsp;d)</CODE>
336
337 <BR>
338 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Verifies that the data set has length of power of 2.</TD>
339 </TR>
340 <TR BGCOLOR="white" CLASS="TableRowColor">
341 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
342 <CODE>static&nbsp;void</CODE></FONT></TD>
343 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#verifyDataSet(java.lang.Object[])">verifyDataSet</A></B>(<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>[]&nbsp;o)</CODE>
344
345 <BR>
346 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Verifies that the data set has length of power of 2.</TD>
347 </TR>
348 <TR BGCOLOR="white" CLASS="TableRowColor">
349 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
350 <CODE>static&nbsp;void</CODE></FONT></TD>
351 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#verifyInterval(double, double)">verifyInterval</A></B>(double&nbsp;lower,
352 double&nbsp;upper)</CODE>
353
354 <BR>
355 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Verifies that the endpoints specify an interval.</TD>
356 </TR>
357 </TABLE>
358 &nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
359 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
360 <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
361 <TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
362 </TR>
363 <TR BGCOLOR="white" CLASS="TableRowColor">
364 <TD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
365 </TR>
366 </TABLE>
367 &nbsp;
368 <P>
369
370 <!-- ========= CONSTRUCTOR DETAIL ======== -->
371
372 <A NAME="constructor_detail"><!-- --></A>
373 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
374 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
375 <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
376 <B>Constructor Detail</B></FONT></TH>
377 </TR>
378 </TABLE>
379
380 <A NAME="FastFourierTransformer()"><!-- --></A><H3>
381 FastFourierTransformer</H3>
382 <PRE>
383 public <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.73"><B>FastFourierTransformer</B></A>()</PRE>
384 <DL>
385 <DD>Construct a default transformer.
386 <P>
387 </DL>
388
389 <!-- ============ METHOD DETAIL ========== -->
390
391 <A NAME="method_detail"><!-- --></A>
392 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
393 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
394 <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
395 <B>Method Detail</B></FONT></TH>
396 </TR>
397 </TABLE>
398
399 <A NAME="transform(double[])"><!-- --></A><H3>
400 transform</H3>
401 <PRE>
402 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.87"><B>transform</B></A>(double[]&nbsp;f)
403 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
404 <DL>
405 <DD>Transform the given real data set.
406 <p>
407 The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $
408 </p>
409 <P>
410 <DD><DL>
411 </DL>
412 </DD>
413 <DD><DL>
414 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the real data array to be transformed
415 <DT><B>Returns:</B><DD>the complex transformed array
416 <DT><B>Throws:</B>
417 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
418 </DD>
419 </DL>
420 <HR>
421
422 <A NAME="transform(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)"><!-- --></A><H3>
423 transform</H3>
424 <PRE>
425 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.107"><B>transform</B></A>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
426 double&nbsp;min,
427 double&nbsp;max,
428 int&nbsp;n)
429 throws <A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A>,
430 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
431 <DL>
432 <DD>Transform the given real function, sampled on the given interval.
433 <p>
434 The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $
435 </p>
436 <P>
437 <DD><DL>
438 </DL>
439 </DD>
440 <DD><DL>
441 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the function to be sampled and transformed<DD><CODE>min</CODE> - the lower bound for the interval<DD><CODE>max</CODE> - the upper bound for the interval<DD><CODE>n</CODE> - the number of sample points
442 <DT><B>Returns:</B><DD>the complex transformed array
443 <DT><B>Throws:</B>
444 <DD><CODE><A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A></CODE> - if function cannot be evaluated
445 at some point
446 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
447 </DD>
448 </DL>
449 <HR>
450
451 <A NAME="transform(org.apache.commons.math.complex.Complex[])"><!-- --></A><H3>
452 transform</H3>
453 <PRE>
454 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.124"><B>transform</B></A>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f)
455 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
456 <DL>
457 <DD>Transform the given complex data set.
458 <p>
459 The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $
460 </p>
461 <P>
462 <DD><DL>
463 </DL>
464 </DD>
465 <DD><DL>
466 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the complex data array to be transformed
467 <DT><B>Returns:</B><DD>the complex transformed array
468 <DT><B>Throws:</B>
469 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
470 </DD>
471 </DL>
472 <HR>
473
474 <A NAME="transform2(double[])"><!-- --></A><H3>
475 transform2</H3>
476 <PRE>
477 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.140"><B>transform2</B></A>(double[]&nbsp;f)
478 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
479 <DL>
480 <DD>Transform the given real data set.
481 <p>
482 The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$
483 </p>
484 <P>
485 <DD><DL>
486 </DL>
487 </DD>
488 <DD><DL>
489 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the real data array to be transformed
490 <DT><B>Returns:</B><DD>the complex transformed array
491 <DT><B>Throws:</B>
492 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
493 </DD>
494 </DL>
495 <HR>
496
497 <A NAME="transform2(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)"><!-- --></A><H3>
498 transform2</H3>
499 <PRE>
500 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.162"><B>transform2</B></A>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
501 double&nbsp;min,
502 double&nbsp;max,
503 int&nbsp;n)
504 throws <A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A>,
505 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
506 <DL>
507 <DD>Transform the given real function, sampled on the given interval.
508 <p>
509 The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$
510 </p>
511 <P>
512 <DD><DL>
513 </DL>
514 </DD>
515 <DD><DL>
516 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the function to be sampled and transformed<DD><CODE>min</CODE> - the lower bound for the interval<DD><CODE>max</CODE> - the upper bound for the interval<DD><CODE>n</CODE> - the number of sample points
517 <DT><B>Returns:</B><DD>the complex transformed array
518 <DT><B>Throws:</B>
519 <DD><CODE><A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A></CODE> - if function cannot be evaluated
520 at some point
521 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
522 </DD>
523 </DL>
524 <HR>
525
526 <A NAME="transform2(org.apache.commons.math.complex.Complex[])"><!-- --></A><H3>
527 transform2</H3>
528 <PRE>
529 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.181"><B>transform2</B></A>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f)
530 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
531 <DL>
532 <DD>Transform the given complex data set.
533 <p>
534 The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$
535 </p>
536 <P>
537 <DD><DL>
538 </DL>
539 </DD>
540 <DD><DL>
541 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the complex data array to be transformed
542 <DT><B>Returns:</B><DD>the complex transformed array
543 <DT><B>Throws:</B>
544 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
545 </DD>
546 </DL>
547 <HR>
548
549 <A NAME="inversetransform(double[])"><!-- --></A><H3>
550 inversetransform</H3>
551 <PRE>
552 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.199"><B>inversetransform</B></A>(double[]&nbsp;f)
553 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
554 <DL>
555 <DD>Inversely transform the given real data set.
556 <p>
557 The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $
558 </p>
559 <P>
560 <DD><DL>
561 </DL>
562 </DD>
563 <DD><DL>
564 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the real data array to be inversely transformed
565 <DT><B>Returns:</B><DD>the complex inversely transformed array
566 <DT><B>Throws:</B>
567 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
568 </DD>
569 </DL>
570 <HR>
571
572 <A NAME="inversetransform(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)"><!-- --></A><H3>
573 inversetransform</H3>
574 <PRE>
575 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.221"><B>inversetransform</B></A>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
576 double&nbsp;min,
577 double&nbsp;max,
578 int&nbsp;n)
579 throws <A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A>,
580 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
581 <DL>
582 <DD>Inversely transform the given real function, sampled on the given interval.
583 <p>
584 The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $
585 </p>
586 <P>
587 <DD><DL>
588 </DL>
589 </DD>
590 <DD><DL>
591 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the function to be sampled and inversely transformed<DD><CODE>min</CODE> - the lower bound for the interval<DD><CODE>max</CODE> - the upper bound for the interval<DD><CODE>n</CODE> - the number of sample points
592 <DT><B>Returns:</B><DD>the complex inversely transformed array
593 <DT><B>Throws:</B>
594 <DD><CODE><A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A></CODE> - if function cannot be evaluated
595 at some point
596 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
597 </DD>
598 </DL>
599 <HR>
600
601 <A NAME="inversetransform(org.apache.commons.math.complex.Complex[])"><!-- --></A><H3>
602 inversetransform</H3>
603 <PRE>
604 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.240"><B>inversetransform</B></A>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f)
605 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
606 <DL>
607 <DD>Inversely transform the given complex data set.
608 <p>
609 The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $
610 </p>
611 <P>
612 <DD><DL>
613 </DL>
614 </DD>
615 <DD><DL>
616 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the complex data array to be inversely transformed
617 <DT><B>Returns:</B><DD>the complex inversely transformed array
618 <DT><B>Throws:</B>
619 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
620 </DD>
621 </DL>
622 <HR>
623
624 <A NAME="inversetransform2(double[])"><!-- --></A><H3>
625 inversetransform2</H3>
626 <PRE>
627 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.258"><B>inversetransform2</B></A>(double[]&nbsp;f)
628 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
629 <DL>
630 <DD>Inversely transform the given real data set.
631 <p>
632 The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$
633 </p>
634 <P>
635 <DD><DL>
636 </DL>
637 </DD>
638 <DD><DL>
639 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the real data array to be inversely transformed
640 <DT><B>Returns:</B><DD>the complex inversely transformed array
641 <DT><B>Throws:</B>
642 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
643 </DD>
644 </DL>
645 <HR>
646
647 <A NAME="inversetransform2(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)"><!-- --></A><H3>
648 inversetransform2</H3>
649 <PRE>
650 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.280"><B>inversetransform2</B></A>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
651 double&nbsp;min,
652 double&nbsp;max,
653 int&nbsp;n)
654 throws <A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A>,
655 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
656 <DL>
657 <DD>Inversely transform the given real function, sampled on the given interval.
658 <p>
659 The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$
660 </p>
661 <P>
662 <DD><DL>
663 </DL>
664 </DD>
665 <DD><DL>
666 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the function to be sampled and inversely transformed<DD><CODE>min</CODE> - the lower bound for the interval<DD><CODE>max</CODE> - the upper bound for the interval<DD><CODE>n</CODE> - the number of sample points
667 <DT><B>Returns:</B><DD>the complex inversely transformed array
668 <DT><B>Throws:</B>
669 <DD><CODE><A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A></CODE> - if function cannot be evaluated
670 at some point
671 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
672 </DD>
673 </DL>
674 <HR>
675
676 <A NAME="inversetransform2(org.apache.commons.math.complex.Complex[])"><!-- --></A><H3>
677 inversetransform2</H3>
678 <PRE>
679 public <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.299"><B>inversetransform2</B></A>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f)
680 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
681 <DL>
682 <DD>Inversely transform the given complex data set.
683 <p>
684 The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$
685 </p>
686 <P>
687 <DD><DL>
688 </DL>
689 </DD>
690 <DD><DL>
691 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the complex data array to be inversely transformed
692 <DT><B>Returns:</B><DD>the complex inversely transformed array
693 <DT><B>Throws:</B>
694 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
695 </DD>
696 </DL>
697 <HR>
698
699 <A NAME="fft(double[], boolean)"><!-- --></A><H3>
700 fft</H3>
701 <PRE>
702 protected <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.315"><B>fft</B></A>(double[]&nbsp;f,
703 boolean&nbsp;isInverse)
704 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
705 <DL>
706 <DD>Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).
707 <P>
708 <DD><DL>
709 </DL>
710 </DD>
711 <DD><DL>
712 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the real data array to be transformed<DD><CODE>isInverse</CODE> - the indicator of forward or inverse transform
713 <DT><B>Returns:</B><DD>the complex transformed array
714 <DT><B>Throws:</B>
715 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
716 </DD>
717 </DL>
718 <HR>
719
720 <A NAME="fft(org.apache.commons.math.complex.Complex[])"><!-- --></A><H3>
721 fft</H3>
722 <PRE>
723 protected <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.360"><B>fft</B></A>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;data)
724 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
725 <DL>
726 <DD>Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).
727 <P>
728 <DD><DL>
729 </DL>
730 </DD>
731 <DD><DL>
732 <DT><B>Parameters:</B><DD><CODE>data</CODE> - the complex data array to be transformed
733 <DT><B>Returns:</B><DD>the complex transformed array
734 <DT><B>Throws:</B>
735 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
736 </DD>
737 </DL>
738 <HR>
739
740 <A NAME="sample(org.apache.commons.math.analysis.UnivariateRealFunction, double, double, int)"><!-- --></A><H3>
741 sample</H3>
742 <PRE>
743 public static double[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.445"><B>sample</B></A>(<A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">UnivariateRealFunction</A>&nbsp;f,
744 double&nbsp;min,
745 double&nbsp;max,
746 int&nbsp;n)
747 throws <A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A>,
748 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
749 <DL>
750 <DD>Sample the given univariate real function on the given interval.
751 <p>
752 The interval is divided equally into N sections and sample points
753 are taken from min to max-(max-min)/N. Usually f(x) is periodic
754 such that f(min) = f(max) (note max is not sampled), but we don't
755 require that.</p>
756 <P>
757 <DD><DL>
758 </DL>
759 </DD>
760 <DD><DL>
761 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the function to be sampled<DD><CODE>min</CODE> - the lower bound for the interval<DD><CODE>max</CODE> - the upper bound for the interval<DD><CODE>n</CODE> - the number of sample points
762 <DT><B>Returns:</B><DD>the samples array
763 <DT><B>Throws:</B>
764 <DD><CODE><A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A></CODE> - if function cannot be evaluated
765 at some point
766 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any parameters are invalid</DL>
767 </DD>
768 </DL>
769 <HR>
770
771 <A NAME="scaleArray(double[], double)"><!-- --></A><H3>
772 scaleArray</H3>
773 <PRE>
774 public static double[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.472"><B>scaleArray</B></A>(double[]&nbsp;f,
775 double&nbsp;d)</PRE>
776 <DL>
777 <DD>Multiply every component in the given real array by the
778 given real number. The change is made in place.
779 <P>
780 <DD><DL>
781 </DL>
782 </DD>
783 <DD><DL>
784 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the real array to be scaled<DD><CODE>d</CODE> - the real scaling coefficient
785 <DT><B>Returns:</B><DD>a reference to the scaled array</DL>
786 </DD>
787 </DL>
788 <HR>
789
790 <A NAME="scaleArray(org.apache.commons.math.complex.Complex[], double)"><!-- --></A><H3>
791 scaleArray</H3>
792 <PRE>
793 public static <A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[] <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.487"><B>scaleArray</B></A>(<A HREF="../../../../../org/apache/commons/math/complex/Complex.html" title="class in org.apache.commons.math.complex">Complex</A>[]&nbsp;f,
794 double&nbsp;d)</PRE>
795 <DL>
796 <DD>Multiply every component in the given complex array by the
797 given real number. The change is made in place.
798 <P>
799 <DD><DL>
800 </DL>
801 </DD>
802 <DD><DL>
803 <DT><B>Parameters:</B><DD><CODE>f</CODE> - the complex array to be scaled<DD><CODE>d</CODE> - the real scaling coefficient
804 <DT><B>Returns:</B><DD>a reference to the scaled array</DL>
805 </DD>
806 </DL>
807 <HR>
808
809 <A NAME="isPowerOf2(long)"><!-- --></A><H3>
810 isPowerOf2</H3>
811 <PRE>
812 public static boolean <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.500"><B>isPowerOf2</B></A>(long&nbsp;n)</PRE>
813 <DL>
814 <DD>Returns true if the argument is power of 2.
815 <P>
816 <DD><DL>
817 </DL>
818 </DD>
819 <DD><DL>
820 <DT><B>Parameters:</B><DD><CODE>n</CODE> - the number to test
821 <DT><B>Returns:</B><DD>true if the argument is power of 2</DL>
822 </DD>
823 </DL>
824 <HR>
825
826 <A NAME="verifyDataSet(double[])"><!-- --></A><H3>
827 verifyDataSet</H3>
828 <PRE>
829 public static void <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.510"><B>verifyDataSet</B></A>(double[]&nbsp;d)
830 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
831 <DL>
832 <DD>Verifies that the data set has length of power of 2.
833 <P>
834 <DD><DL>
835 </DL>
836 </DD>
837 <DD><DL>
838 <DT><B>Parameters:</B><DD><CODE>d</CODE> - the data array
839 <DT><B>Throws:</B>
840 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if array length is not power of 2</DL>
841 </DD>
842 </DL>
843 <HR>
844
845 <A NAME="verifyDataSet(java.lang.Object[])"><!-- --></A><H3>
846 verifyDataSet</H3>
847 <PRE>
848 public static void <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.523"><B>verifyDataSet</B></A>(<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>[]&nbsp;o)
849 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
850 <DL>
851 <DD>Verifies that the data set has length of power of 2.
852 <P>
853 <DD><DL>
854 </DL>
855 </DD>
856 <DD><DL>
857 <DT><B>Parameters:</B><DD><CODE>o</CODE> - the data array
858 <DT><B>Throws:</B>
859 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if array length is not power of 2</DL>
860 </DD>
861 </DL>
862 <HR>
863
864 <A NAME="verifyInterval(double, double)"><!-- --></A><H3>
865 verifyInterval</H3>
866 <PRE>
867 public static void <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.537"><B>verifyInterval</B></A>(double&nbsp;lower,
868 double&nbsp;upper)
869 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
870 <DL>
871 <DD>Verifies that the endpoints specify an interval.
872 <P>
873 <DD><DL>
874 </DL>
875 </DD>
876 <DD><DL>
877 <DT><B>Parameters:</B><DD><CODE>lower</CODE> - lower endpoint<DD><CODE>upper</CODE> - upper endpoint
878 <DT><B>Throws:</B>
879 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if not interval</DL>
880 </DD>
881 </DL>
882 <HR>
883
884 <A NAME="mdfft(java.lang.Object, boolean)"><!-- --></A><H3>
885 mdfft</H3>
886 <PRE>
887 public <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A> <A HREF="../../../../../src-html/org/apache/commons/math/transform/FastFourierTransformer.html#line.561"><B>mdfft</B></A>(<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>&nbsp;mdca,
888 boolean&nbsp;forward)
889 throws <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
890 <DL>
891 <DD>Performs a multi-dimensional Fourier transform on a given array.
892 Use <A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#inversetransform2(org.apache.commons.math.complex.Complex[])"><CODE>inversetransform2(Complex[])</CODE></A> and
893 <A HREF="../../../../../org/apache/commons/math/transform/FastFourierTransformer.html#transform2(org.apache.commons.math.complex.Complex[])"><CODE>transform2(Complex[])</CODE></A> in a row-column implementation
894 in any number of dimensions with O(N&times;log(N)) complexity with
895 N=n<sub>1</sub>&times;n<sub>2</sub>&times;n<sub>3</sub>&times;...&times;n<sub>d</sub>,
896 n<sub>x</sub>=number of elements in dimension x,
897 and d=total number of dimensions.
898 <P>
899 <DD><DL>
900 </DL>
901 </DD>
902 <DD><DL>
903 <DT><B>Parameters:</B><DD><CODE>mdca</CODE> - Multi-Dimensional Complex Array id est Complex[][][][]<DD><CODE>forward</CODE> - inverseTransform2 is preformed if this is false
904 <DT><B>Returns:</B><DD>transform of mdca as a Multi-Dimensional Complex Array id est Complex[][][][]
905 <DT><B>Throws:</B>
906 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if any dimension is not a power of two</DL>
907 </DD>
908 </DL>
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