1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>The Wavelet object — PyWavelets Documentation</title>
<link rel="stylesheet" href="../_static/default.css" type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: '../',
VERSION: '0.2.0',
COLLAPSE_MODINDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true
};
</script>
<script type="text/javascript" src="../_static/jquery.js"></script>
<script type="text/javascript" src="../_static/doctools.js"></script>
<link rel="shortcut icon" href="../_static/favicon.ico"/>
<link rel="top" title="PyWavelets Documentation" href="../index.html" />
<link rel="up" title="Usage examples" href="index.html" />
<link rel="next" title="Signal Extension Modes" href="modes.html" />
<link rel="prev" title="Usage examples" href="index.html" />
<meta name="description" content="PyWavelets is a scientific Python module for Wavelet Transform calculations." />
<meta name="keywords" content="PyWavelets, wavelets, Python, wavelet transform, discrete wavelet transform, dwt, idwt, swt, wavelet packets, stationary wavelet transform, pywt, Filip Wasilewski" />
<meta name="author" content="Filip Wasilewski" />
<meta name="Distribution" content="Global" />
<meta name="Robots" content="INDEX,FOLLOW" />
</head>
<body>
<div class="related">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="../modindex.html" title="Global Module Index"
accesskey="M">modules</a> |</li>
<li class="right" >
<a href="modes.html" title="Signal Extension Modes"
accesskey="N">next</a> |</li>
<li class="right" >
<a href="index.html" title="Usage examples"
accesskey="P">previous</a> |</li>
<li><a href="../index.html">PyWavelets Documentation</a> »</li>
<li><a href="index.html" accesskey="U">Usage examples</a> »</li>
</ul>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body">
<div class="section" id="the-wavelet-object">
<span id="reg-wavelet"></span><h1>The Wavelet object<a class="headerlink" href="#the-wavelet-object" title="Permalink to this headline">¶</a></h1>
<div class="section" id="wavelet-families-and-builtin-wavelets-names">
<h2>Wavelet families and builtin Wavelets names<a class="headerlink" href="#wavelet-families-and-builtin-wavelets-names" title="Permalink to this headline">¶</a></h2>
<p><a title="pywt.Wavelet" class="reference external" href="../ref/wavelets.html#pywt.Wavelet"><tt class="xref docutils literal"><span class="pre">Wavelet</span></tt></a> objects are really a handy carriers of a bunch of DWT-specific
data like <em>quadrature mirror filters</em> and some general properties associated
with them.</p>
<p>At first let’s go through the methods of creating a <a title="pywt.Wavelet" class="reference external" href="../ref/wavelets.html#pywt.Wavelet"><tt class="xref docutils literal"><span class="pre">Wavelet</span></tt></a> object.
The easiest and the most convenient way is to use builtin named Wavelets.</p>
<p>These wavelets are organized into groups called wavelet families. The most
commonly used families are:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pywt</span>
<span class="gp">>>> </span><span class="n">pywt</span><span class="o">.</span><span class="n">families</span><span class="p">()</span>
<span class="go">['haar', 'db', 'sym', 'coif', 'bior', 'rbio', 'dmey']</span>
</pre></div>
</div>
<p>The <a title="pywt.wavelist" class="reference external" href="../ref/wavelets.html#pywt.wavelist"><tt class="xref docutils literal"><span class="pre">wavelist()</span></tt></a> function with family name passed as an argument is used to
obtain the list of wavelet names in each family.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">for</span> <span class="n">family</span> <span class="ow">in</span> <span class="n">pywt</span><span class="o">.</span><span class="n">families</span><span class="p">():</span>
<span class="gp">... </span> <span class="k">print</span> <span class="s">"</span><span class="si">%s</span><span class="s"> family:"</span> <span class="o">%</span> <span class="n">family</span><span class="p">,</span> <span class="s">', '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">pywt</span><span class="o">.</span><span class="n">wavelist</span><span class="p">(</span><span class="n">family</span><span class="p">))</span>
<span class="go">haar family: haar</span>
<span class="go">db family: db1, db2, db3, db4, db5, db6, db7, db8, db9, db10, db11, db12, db13, db14, db15, db16, db17, db18, db19, db20</span>
<span class="go">sym family: sym2, sym3, sym4, sym5, sym6, sym7, sym8, sym9, sym10, sym11, sym12, sym13, sym14, sym15, sym16, sym17, sym18, sym19, sym20</span>
<span class="go">coif family: coif1, coif2, coif3, coif4, coif5</span>
<span class="go">bior family: bior1.1, bior1.3, bior1.5, bior2.2, bior2.4, bior2.6, bior2.8, bior3.1, bior3.3, bior3.5, bior3.7, bior3.9, bior4.4, bior5.5, bior6.8</span>
<span class="go">rbio family: rbio1.1, rbio1.3, rbio1.5, rbio2.2, rbio2.4, rbio2.6, rbio2.8, rbio3.1, rbio3.3, rbio3.5, rbio3.7, rbio3.9, rbio4.4, rbio5.5, rbio6.8</span>
<span class="go">dmey family: dmey</span>
</pre></div>
</div>
<p>To get the full list of builtin wavelets’ names just use the <a title="pywt.wavelist" class="reference external" href="../ref/wavelets.html#pywt.wavelist"><tt class="xref docutils literal"><span class="pre">wavelist()</span></tt></a>
with no argument. As you can see currently there are 76 builtin wavelets.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">pywt</span><span class="o">.</span><span class="n">wavelist</span><span class="p">())</span>
<span class="go">76</span>
</pre></div>
</div>
</div>
<div class="section" id="creating-wavelet-objects">
<h2>Creating Wavelet objects<a class="headerlink" href="#creating-wavelet-objects" title="Permalink to this headline">¶</a></h2>
<p>Now when we know all the names let’s finnally create a <a title="pywt.Wavelet" class="reference external" href="../ref/wavelets.html#pywt.Wavelet"><tt class="xref docutils literal"><span class="pre">Wavelet</span></tt></a> object:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">w</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s">'db3'</span><span class="p">)</span>
</pre></div>
</div>
<p>So.. that’s it.</p>
</div>
<div class="section" id="wavelet-properties">
<h2>Wavelet properties<a class="headerlink" href="#wavelet-properties" title="Permalink to this headline">¶</a></h2>
<p>But what can we do with <a title="pywt.Wavelet" class="reference external" href="../ref/wavelets.html#pywt.Wavelet"><tt class="xref docutils literal"><span class="pre">Wavelet</span></tt></a> objects? Well, they carry some
interresting information.</p>
<p>First, let’s try printing a <a title="pywt.Wavelet" class="reference external" href="../ref/wavelets.html#pywt.Wavelet"><tt class="xref docutils literal"><span class="pre">Wavelet</span></tt></a> object. This shows a brief
information about it’s name, it’s family name and some properties like
orthogonality and symmetry.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">w</span>
<span class="go">Wavelet db3</span>
<span class="go"> Family name: Daubechies</span>
<span class="go"> Short name: db</span>
<span class="go"> Filters length: 6</span>
<span class="go"> Orthogonal: True</span>
<span class="go"> Biorthogonal: True</span>
<span class="go"> Symmetry: asymmetric</span>
</pre></div>
</div>
<p>But the most important information are the wavelet filters coefficients, which
are used in <a class="reference external" href="../ref/dwt-discrete-wavelet-transform.html#ref-dwt"><em>Discrete Wavelet Transform</em></a>. These coefficients can
be obtained via the <a title="pywt.Wavelet.dec_lo" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.dec_lo"><tt class="xref docutils literal"><span class="pre">dec_lo</span></tt></a>, <a title="pywt.Wavelet.dec_hi" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.dec_hi"><tt class="xref docutils literal"><span class="pre">Wavelet.dec_hi</span></tt></a>,
<a title="pywt.Wavelet.rec_lo" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.rec_lo"><tt class="xref docutils literal"><span class="pre">rec_lo</span></tt></a> and <a title="pywt.Wavelet.rec_hi" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.rec_hi"><tt class="xref docutils literal"><span class="pre">rec_hi</span></tt></a> attributes, which
corresponds to lowpass and highpass decomposition filters and lowpass and
highpass reconstruction filters respectively:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">dec_lo</span>
<span class="go">[0.035226291882100656, -0.085441273882241486, -0.13501102001039084, 0.45987750211933132, 0.80689150931333875, 0.33267055295095688]</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">dec_hi</span>
<span class="go">[-0.33267055295095688, 0.80689150931333875, -0.45987750211933132, -0.13501102001039084, 0.085441273882241486, 0.035226291882100656]</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">rec_lo</span>
<span class="go">[0.33267055295095688, 0.80689150931333875, 0.45987750211933132, -0.13501102001039084, -0.085441273882241486, 0.035226291882100656]</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">rec_hi</span>
<span class="go">[0.035226291882100656, 0.085441273882241486, -0.13501102001039084, -0.45987750211933132, 0.80689150931333875, -0.33267055295095688]</span>
</pre></div>
</div>
<p>Another way to get the filters data is to use the <a title="pywt.Wavelet.filter_bank" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.filter_bank"><tt class="xref docutils literal"><span class="pre">filter_bank</span></tt></a>
attribute, which returns all four filters in a tuple:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">filter_bank</span> <span class="o">==</span> <span class="p">(</span><span class="n">w</span><span class="o">.</span><span class="n">dec_lo</span><span class="p">,</span> <span class="n">w</span><span class="o">.</span><span class="n">dec_hi</span><span class="p">,</span> <span class="n">w</span><span class="o">.</span><span class="n">rec_lo</span><span class="p">,</span> <span class="n">w</span><span class="o">.</span><span class="n">rec_hi</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
<p>Other Wavelet’s properties are:</p>
<blockquote>
<p>Wavelet <a title="pywt.Wavelet.name" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.name"><tt class="xref docutils literal"><span class="pre">name</span></tt></a>, <a title="pywt.Wavelet.short_family_name" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.short_family_name"><tt class="xref docutils literal"><span class="pre">short_family_name</span></tt></a> and <a title="pywt.Wavelet.family_name" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.family_name"><tt class="xref docutils literal"><span class="pre">family_name</span></tt></a>:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">w</span><span class="o">.</span><span class="n">name</span>
<span class="go">db3</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="n">w</span><span class="o">.</span><span class="n">short_family_name</span>
<span class="go">db</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="n">w</span><span class="o">.</span><span class="n">family_name</span>
<span class="go">Daubechies</span>
</pre></div>
</div>
<ul>
<li><p class="first">Decomposition (<a title="pywt.Wavelet.dec_len" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.dec_len"><tt class="xref docutils literal"><span class="pre">dec_len</span></tt></a>) and reconstruction
(<a title="pywt.Wavelet.rec_len" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.rec_len"><tt class="xref docutils literal"><span class="pre">rec_len</span></tt></a>) filter lengths:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">dec_len</span>
<span class="go">6</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">rec_len</span>
<span class="go">6</span>
</pre></div>
</div>
</li>
<li><p class="first">Orthogonality (<a title="pywt.Wavelet.orthogonal" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.orthogonal"><tt class="xref docutils literal"><span class="pre">orthogonal</span></tt></a>) and biorthogonality (<a title="pywt.Wavelet.biorthogonal" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.biorthogonal"><tt class="xref docutils literal"><span class="pre">biorthogonal</span></tt></a>):</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">orthogonal</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">biorthogonal</span>
<span class="go">True</span>
</pre></div>
</div>
</li>
<li><p class="first">Symmetry (<a title="pywt.Wavelet.symmetry" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.symmetry"><tt class="xref docutils literal"><span class="pre">symmetry</span></tt></a>):</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">w</span><span class="o">.</span><span class="n">symmetry</span>
<span class="go">asymmetric</span>
</pre></div>
</div>
</li>
<li><p class="first">Number of vanishing moments for the scaling function <em>phi</em>
(<a title="pywt.Wavelet.vanishing_moments_phi" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.vanishing_moments_phi"><tt class="xref docutils literal"><span class="pre">vanishing_moments_phi</span></tt></a>) and the wavelet function <em>psi</em>
(<a title="pywt.Wavelet.vanishing_moments_psi" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.vanishing_moments_psi"><tt class="xref docutils literal"><span class="pre">vanishing_moments_psi</span></tt></a>) associated with the filters:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">vanishing_moments_phi</span>
<span class="go">0</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">vanishing_moments_psi</span>
<span class="go">3</span>
</pre></div>
</div>
</li>
</ul>
</blockquote>
<p>Now when we know a bit about the builtin Wavelets, les’t see how to create
<a class="reference external" href="../ref/wavelets.html#custom-wavelets"><em>custom Wavelets</em></a> objects. These can be done in two ways:</p>
<blockquote>
<ol class="arabic">
<li><p class="first">Passing the filter bank object that implements the <cite>filter_bank</cite>
attribute. The attribute must return four filters coefficients.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">class</span> <span class="nc">MyHaarFilterBank</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="gp">... </span> <span class="nd">@property</span>
<span class="gp">... </span> <span class="k">def</span> <span class="nf">filter_bank</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="gp">... </span> <span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
<span class="gp">... </span> <span class="k">return</span> <span class="p">([</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">my_wavelet</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s">'My Haar Wavelet'</span><span class="p">,</span> <span class="n">filter_bank</span><span class="o">=</span><span class="n">MyHaarFilterBank</span><span class="p">())</span>
</pre></div>
</div>
</li>
<li><p class="first">Passing the filters coefficients directly as the <em>filter_bank</em> parameter.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
<span class="gp">>>> </span><span class="n">my_filter_bank</span> <span class="o">=</span> <span class="p">([</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">my_wavelet</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s">'My Haar Wavelet'</span><span class="p">,</span> <span class="n">filter_bank</span><span class="o">=</span><span class="n">my_filter_bank</span><span class="p">)</span>
</pre></div>
</div>
</li>
</ol>
</blockquote>
<p>Note that such custom wavelets <strong>will not</strong> have all the properties set
to correct values:</p>
<blockquote>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">my_wavelet</span>
<span class="go">Wavelet My Haar Wavelet</span>
<span class="go"> Family name:</span>
<span class="go"> Short name:</span>
<span class="go"> Filters length: 2</span>
<span class="go"> Orthogonal: False</span>
<span class="go"> Biorthogonal: False</span>
<span class="go"> Symmetry: unknown</span>
</pre></div>
</div>
<p>You can hovewer set a few of them on your own:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">my_wavelet</span><span class="o">.</span><span class="n">orthogonal</span> <span class="o">=</span> <span class="bp">True</span>
<span class="gp">>>> </span><span class="n">my_wavelet</span><span class="o">.</span><span class="n">biorthogonal</span> <span class="o">=</span> <span class="bp">True</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">my_wavelet</span>
<span class="go">Wavelet My Haar Wavelet</span>
<span class="go"> Family name:</span>
<span class="go"> Short name:</span>
<span class="go"> Filters length: 2</span>
<span class="go"> Orthogonal: True</span>
<span class="go"> Biorthogonal: True</span>
<span class="go"> Symmetry: unknown</span>
</pre></div>
</div>
</blockquote>
</div>
<div class="section" id="and-now-the-wavefun">
<h2>And now... the <cite>wavefun</cite>!<a class="headerlink" href="#and-now-the-wavefun" title="Permalink to this headline">¶</a></h2>
<p>We all know that the fun with wavelets is in wavelet functions.
Now what would be this package without a tool to compute wavelet
and scaling functions approximations?</p>
<p>This is the purpose of the <a title="pywt.Wavelet.wavefun" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.wavefun"><tt class="xref docutils literal"><span class="pre">wavefun()</span></tt></a> method, which is used to
approximate scaling function (<em>phi</em>) and wavelet function (<em>psi</em>) at the given
level of refinement, based on the filters coefficients.</p>
<p>The number of returned values varies depending on the wavelet’s
orthogonality property. For orthogonal wavelets the result is tuple
with scaling function, wavelet function and xgrid coordinates.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">w</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s">'sym3'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">orthogonal</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="p">(</span><span class="n">phi</span><span class="p">,</span> <span class="n">psi</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="n">w</span><span class="o">.</span><span class="n">wavefun</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
<p>For biorthogonal (non-orthogonal) wavelets different scaling and wavelet
functions are used for decomposition and reconstruction, and thus five
elements are returned: decomposition scaling and wavelet functions
approximations, reconstruction scaling and wavelet functions approximations,
and the xgrid.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">w</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">Wavelet</span><span class="p">(</span><span class="s">'bior1.3'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">w</span><span class="o">.</span><span class="n">orthogonal</span>
<span class="go">False</span>
<span class="gp">>>> </span><span class="p">(</span><span class="n">phi_d</span><span class="p">,</span> <span class="n">psi_d</span><span class="p">,</span> <span class="n">phi_r</span><span class="p">,</span> <span class="n">psi_r</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="n">w</span><span class="o">.</span><span class="n">wavefun</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
<div class="admonition-see-also admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last">You can find live examples of <a title="pywt.Wavelet.wavefun" class="reference external" href="../ref/wavelets.html#pywt.Wavelet.wavefun"><tt class="xref docutils literal"><span class="pre">wavefun()</span></tt></a> usage and
images of all the built-in wavelets on the
<a class="reference external" href="http://wavelets.pybytes.com">Wavelet Properties Browser</a> page.</p>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="sphinxsidebar">
<div class="sphinxsidebarwrapper">
<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference external" href="#">The Wavelet object</a><ul>
<li><a class="reference external" href="#wavelet-families-and-builtin-wavelets-names">Wavelet families and builtin Wavelets names</a></li>
<li><a class="reference external" href="#creating-wavelet-objects">Creating Wavelet objects</a></li>
<li><a class="reference external" href="#wavelet-properties">Wavelet properties</a></li>
<li><a class="reference external" href="#and-now-the-wavefun">And now... the <cite>wavefun</cite>!</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
<p class="topless"><a href="index.html"
title="previous chapter">Usage examples</a></p>
<h4>Next topic</h4>
<p class="topless"><a href="modes.html"
title="next chapter">Signal Extension Modes</a></p>
<h3>This Page</h3>
<ul class="this-page-menu">
<li><a href="../_sources/regression/wavelet.txt"
rel="nofollow">Show Source</a></li>
</ul>
<div id="searchbox" style="display: none">
<h3>Quick search</h3>
<form class="search" action="../search.html" method="get">
<input type="text" name="q" size="18" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
<p class="searchtip" style="font-size: 90%">
Enter search terms or a module, class or function name.
</p>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
<div>
<h3>Quick links</h3>
<ul>
<li><a href="http://groups.google.com/group/pywavelets"><img src="../_static/comments.png" height="16" width="16" alt="" /> Visit Discussion Group</a></li>
<li><a href="http://wavelets.scipy.org/moin/"><img src="../_static/page_edit.png" height="16" width="16" alt="" /> View Wiki Page</a></li>
<li><a href="http://projects.scipy.org/wavelets/browser/pywt/trunk/"><img src="../_static/cog.png" height="16" width="16" alt="" /> Browse Source Code</a></li>
<li><a href="http://wavelets.pybytes.com/"><img src="../_static/wave.png" height="16" width="16" alt="" /> Explore Wavelets</a></li>
<li><a href="http://delicious.com/save" onclick="window.open('http://delicious.com/save?v=5&noui&jump=close&url='+encodeURIComponent('http://www.pybytes.com/pywavelets/')+'&title='+encodeURIComponent('PyWavelets - Discrete Wavelet Transform in Python'), 'delicious','toolbar=no,width=550,height=550'); return false;"><img src="../_static/delicious.png" height="12" width="12" alt="Delicious" style="margin: 0 2px 0 2px;" /> Bookmark with Delicious</a></li>
<li><a href="http://twitter.com/filipwasilewski"><img src="../_static/twitter.png" height="16" width="16" alt="" /> Follow on Twitter</a></li>
</ul>
</div>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="related">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="General Index"
>index</a></li>
<li class="right" >
<a href="../modindex.html" title="Global Module Index"
>modules</a> |</li>
<li class="right" >
<a href="modes.html" title="Signal Extension Modes"
>next</a> |</li>
<li class="right" >
<a href="index.html" title="Usage examples"
>previous</a> |</li>
<li><a href="../index.html">PyWavelets Documentation</a> »</li>
<li><a href="index.html" >Usage examples</a> »</li>
</ul>
</div>
<div class="footer">
© Copyright 2006-2010, <a href="http://filipwasilewski.pl/">Filip Wasilewski</a>.
Last updated on Mar 16, 2010.
Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 0.6.5.
</div>
<script type="text/javascript">
var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www.");
document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E"));
</script>
<script type="text/javascript">
var pageTracker = _gat._getTracker("UA-3396395-3");
pageTracker._initData();
pageTracker._trackPageview();
</script>
</body>
</html>
|
