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60<div class="contents">
61<h1>Windowing<br>
62<small>
63[<a class="el" href="group__signal.html">Signal Processing (SP) Module</a>]</small>
64</h1>Windowing functions. 
65<a href="#_details">More...</a>
66<p>
67<table border="0" cellpadding="0" cellspacing="0">
68<tr><td></td></tr>
69<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
70<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__windfunc.html#g2aaacf0d9be2e3734d3aa091de6f31d1">itpp::hamming</a> (int size)</td></tr>
71
72<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Hamming window.  <a href="#g2aaacf0d9be2e3734d3aa091de6f31d1"></a><br></td></tr>
73<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__windfunc.html#g20d24c3874b219df8226dd5f1a4b66a4">itpp::hanning</a> (int n)</td></tr>
74
75<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Hanning window.  <a href="#g20d24c3874b219df8226dd5f1a4b66a4"></a><br></td></tr>
76<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__windfunc.html#gddea06e93eb4661df1a28236e1cf9393">itpp::hann</a> (int n)</td></tr>
77
78<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Hanning window compatible with matlab.  <a href="#gddea06e93eb4661df1a28236e1cf9393"></a><br></td></tr>
79<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__windfunc.html#g2f6b06232e3652a8ab3874b24ef3bf4e">itpp::blackman</a> (int n)</td></tr>
80
81<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Blackman window.  <a href="#g2f6b06232e3652a8ab3874b24ef3bf4e"></a><br></td></tr>
82<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__windfunc.html#gc69272c4edb22cd46c0ac01d083ba44f">itpp::triang</a> (int n)</td></tr>
83
84<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Triangular window.  <a href="#gc69272c4edb22cd46c0ac01d083ba44f"></a><br></td></tr>
85<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__windfunc.html#g252e21a30783a72a4599802b4b510e08">itpp::sqrt_win</a> (int n)</td></tr>
86
87<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Square root window.  <a href="#g252e21a30783a72a4599802b4b510e08"></a><br></td></tr>
88<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__windfunc.html#g823202ba1d4ad2c82bab016755ede5c0">itpp::chebwin</a> (int n, double at)</td></tr>
89
90<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Dolph-Chebyshev window.  <a href="#g823202ba1d4ad2c82bab016755ede5c0"></a><br></td></tr>
91</table>
92<hr><a name="_details"></a><h2>Detailed Description</h2>
93Windowing functions. <hr><h2>Function Documentation</h2>
94<a class="anchor" name="g2f6b06232e3652a8ab3874b24ef3bf4e"></a><!-- doxytag: member="itpp::blackman" ref="g2f6b06232e3652a8ab3874b24ef3bf4e" args="(int n)" -->
95<div class="memitem">
96<div class="memproto">
97      <table class="memname">
98        <tr>
99          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::blackman           </td>
100          <td>(</td>
101          <td class="paramtype">int&nbsp;</td>
102          <td class="paramname"> <em>n</em>          </td>
103          <td>&nbsp;)&nbsp;</td>
104          <td></td>
105        </tr>
106      </table>
107</div>
108<div class="memdoc">
109
110<p>
111Blackman window.
112<p>
113The <code>n</code> size Blackman window is a vector <img class="formulaInl" alt="$w$" src="form_85.png"> where the <img class="formulaInl" alt="$i$" src="form_366.png">th component is <p class="formulaDsp">
114<img class="formulaDsp" alt="\[ w_i = 0.42 - 0.5\cos(2\pi i/(n-1)) + 0.08\cos(4\pi i/(n-1)) \]" src="form_370.png">
115<p>
116 
117<p>References <a class="el" href="trig__hyp_8h-source.html#l00061">itpp::cos()</a>.</p>
118
119</div>
120</div><p>
121<a class="anchor" name="g823202ba1d4ad2c82bab016755ede5c0"></a><!-- doxytag: member="itpp::chebwin" ref="g823202ba1d4ad2c82bab016755ede5c0" args="(int n, double at)" -->
122<div class="memitem">
123<div class="memproto">
124      <table class="memname">
125        <tr>
126          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::chebwin           </td>
127          <td>(</td>
128          <td class="paramtype">int&nbsp;</td>
129          <td class="paramname"> <em>n</em>, </td>
130        </tr>
131        <tr>
132          <td class="paramkey"></td>
133          <td></td>
134          <td class="paramtype">double&nbsp;</td>
135          <td class="paramname"> <em>at</em></td><td>&nbsp;</td>
136        </tr>
137        <tr>
138          <td></td>
139          <td>)</td>
140          <td></td><td></td><td></td>
141        </tr>
142      </table>
143</div>
144<div class="memdoc">
145
146<p>
147Dolph-Chebyshev window.
148<p>
149The length <code>n</code> Dolph-Chebyshev window is a vector <img class="formulaInl" alt="$w$" src="form_85.png"> whose <img class="formulaInl" alt="$i$" src="form_366.png">th transform component is given by <p class="formulaDsp">
150<img class="formulaDsp" alt="\[ W[k] = \frac{T_M\left(\beta \cos\left(\frac{\pi k}{M}\right) \right)}{T_M(\beta)},k = 0, 1, 2, \ldots, M - 1 \]" src="form_373.png">
151<p>
152 where <code>T_n(x)</code> is the order <code>n</code> Chebyshev polynomial of the first kind.<p>
153<dl compact><dt><b>Parameters:</b></dt><dd>
154  <table border="0" cellspacing="2" cellpadding="0">
155    <tr><td valign="top"></td><td valign="top"><em>n</em>&nbsp;</td><td>length of the Doplh-Chebyshev window </td></tr>
156    <tr><td valign="top"></td><td valign="top"><em>at</em>&nbsp;</td><td>attenutation of side lobe (in dB) </td></tr>
157  </table>
158</dl>
159<dl class="return" compact><dt><b>Returns:</b></dt><dd>symmetric length <code>n</code> Doplh-Chebyshev window</dd></dl>
160<dl class="author" compact><dt><b>Author:</b></dt><dd>Kumar Appaiah and Adam Piatyszek (code review) </dd></dl>
161
162<p>References <a class="el" href="trig__hyp_8h-source.html#l00108">itpp::acosh()</a>, <a class="el" href="poly_8cpp-source.html#l00220">itpp::cheb()</a>, <a class="el" href="trig__hyp_8h-source.html#l00061">itpp::cos()</a>, <a class="el" href="trig__hyp_8h-source.html#l00096">itpp::cosh()</a>, <a class="el" href="group__fft.html#g032f33ed9bd8e7b794c6ee2eb3456f68">itpp::ifft_real()</a>, <a class="el" href="misc_8h-source.html#l00122">itpp::is_even()</a>, <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, <a class="el" href="specmat_8cpp-source.html#l00114">itpp::linspace()</a>, <a class="el" href="log__exp_8h-source.html#l00215">itpp::pow10()</a>, <a class="el" href="matfunc_8h-source.html#l00777">itpp::reverse()</a>, <a class="el" href="vec_8h-source.html#l01319">itpp::Vec&lt; Num_T &gt;::right()</a>, <a class="el" href="trig__hyp_8h-source.html#l00057">itpp::sin()</a>, and <a class="el" href="fix__functions_8cpp-source.html#l00045">itpp::to_cvec()</a>.</p>
163
164</div>
165</div><p>
166<a class="anchor" name="g2aaacf0d9be2e3734d3aa091de6f31d1"></a><!-- doxytag: member="itpp::hamming" ref="g2aaacf0d9be2e3734d3aa091de6f31d1" args="(int size)" -->
167<div class="memitem">
168<div class="memproto">
169      <table class="memname">
170        <tr>
171          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::hamming           </td>
172          <td>(</td>
173          <td class="paramtype">int&nbsp;</td>
174          <td class="paramname"> <em>size</em>          </td>
175          <td>&nbsp;)&nbsp;</td>
176          <td></td>
177        </tr>
178      </table>
179</div>
180<div class="memdoc">
181
182<p>
183Hamming window.
184<p>
185The <code>n</code> size Hamming window is a vector <img class="formulaInl" alt="$w$" src="form_85.png"> where the <img class="formulaInl" alt="$i$" src="form_366.png">th component is <p class="formulaDsp">
186<img class="formulaDsp" alt="\[ w_i = 0.54 - 0.46 \cos(2\pi i/(n-1)) \]" src="form_367.png">
187<p>
188 
189<p>References <a class="el" href="trig__hyp_8h-source.html#l00061">itpp::cos()</a>.</p>
190
191<p>Referenced by <a class="el" href="filter_8cpp-source.html#l00243">itpp::fir1()</a>, and <a class="el" href="channel_8cpp-source.html#l00445">itpp::FIR_Fading_Generator::Jakes_filter()</a>.</p>
192
193</div>
194</div><p>
195<a class="anchor" name="gddea06e93eb4661df1a28236e1cf9393"></a><!-- doxytag: member="itpp::hann" ref="gddea06e93eb4661df1a28236e1cf9393" args="(int n)" -->
196<div class="memitem">
197<div class="memproto">
198      <table class="memname">
199        <tr>
200          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::hann           </td>
201          <td>(</td>
202          <td class="paramtype">int&nbsp;</td>
203          <td class="paramname"> <em>n</em>          </td>
204          <td>&nbsp;)&nbsp;</td>
205          <td></td>
206        </tr>
207      </table>
208</div>
209<div class="memdoc">
210
211<p>
212Hanning window compatible with matlab.
213<p>
214The <code>n</code> size Hanning window is a vector <img class="formulaInl" alt="$w$" src="form_85.png"> where the <img class="formulaInl" alt="$i$" src="form_366.png">th component is <p class="formulaDsp">
215<img class="formulaDsp" alt="\[ w_i = 0.5(1 - \cos(2\pi i/(n-1)) \]" src="form_369.png">
216<p>
217 
218<p>References <a class="el" href="trig__hyp_8h-source.html#l00061">itpp::cos()</a>.</p>
219
220</div>
221</div><p>
222<a class="anchor" name="g20d24c3874b219df8226dd5f1a4b66a4"></a><!-- doxytag: member="itpp::hanning" ref="g20d24c3874b219df8226dd5f1a4b66a4" args="(int n)" -->
223<div class="memitem">
224<div class="memproto">
225      <table class="memname">
226        <tr>
227          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::hanning           </td>
228          <td>(</td>
229          <td class="paramtype">int&nbsp;</td>
230          <td class="paramname"> <em>n</em>          </td>
231          <td>&nbsp;)&nbsp;</td>
232          <td></td>
233        </tr>
234      </table>
235</div>
236<div class="memdoc">
237
238<p>
239Hanning window.
240<p>
241The <code>n</code> size Hanning window is a vector <img class="formulaInl" alt="$w$" src="form_85.png"> where the <img class="formulaInl" alt="$i$" src="form_366.png">th component is <p class="formulaDsp">
242<img class="formulaDsp" alt="\[ w_i = 0.5(1 - \cos(2\pi (i+1)/(n+1)) \]" src="form_368.png">
243<p>
244<p>
245Observe that this function is not the same as the <a class="el" href="group__windfunc.html#gddea06e93eb4661df1a28236e1cf9393" title="Hanning window compatible with matlab.">hann()</a> function which is defined as in matlab.
246<p>References <a class="el" href="trig__hyp_8h-source.html#l00061">itpp::cos()</a>.</p>
247
248<p>Referenced by <a class="el" href="sigfun_8cpp-source.html#l00268">itpp::spectrum()</a>.</p>
249
250</div>
251</div><p>
252<a class="anchor" name="g252e21a30783a72a4599802b4b510e08"></a><!-- doxytag: member="itpp::sqrt_win" ref="g252e21a30783a72a4599802b4b510e08" args="(int n)" -->
253<div class="memitem">
254<div class="memproto">
255      <table class="memname">
256        <tr>
257          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::sqrt_win           </td>
258          <td>(</td>
259          <td class="paramtype">int&nbsp;</td>
260          <td class="paramname"> <em>n</em>          </td>
261          <td>&nbsp;)&nbsp;</td>
262          <td></td>
263        </tr>
264      </table>
265</div>
266<div class="memdoc">
267
268<p>
269Square root window.
270<p>
271The square-root of the Triangle window. sqrt_win(n) = sqrt(triang(n))
272<p>References <a class="el" href="elem__math_8h-source.html#l00126">itpp::sqrt()</a>.</p>
273
274</div>
275</div><p>
276<a class="anchor" name="gc69272c4edb22cd46c0ac01d083ba44f"></a><!-- doxytag: member="itpp::triang" ref="gc69272c4edb22cd46c0ac01d083ba44f" args="(int n)" -->
277<div class="memitem">
278<div class="memproto">
279      <table class="memname">
280        <tr>
281          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::triang           </td>
282          <td>(</td>
283          <td class="paramtype">int&nbsp;</td>
284          <td class="paramname"> <em>n</em>          </td>
285          <td>&nbsp;)&nbsp;</td>
286          <td></td>
287        </tr>
288      </table>
289</div>
290<div class="memdoc">
291
292<p>
293Triangular window.
294<p>
295The <code>n</code> size triangle window is a vector <img class="formulaInl" alt="$w$" src="form_85.png"> where the <img class="formulaInl" alt="$i$" src="form_366.png">th component is <p class="formulaDsp">
296<img class="formulaDsp" alt="\[ w_i = w_{n-i-1} = \frac{2(i+1)}{n+1} \]" src="form_371.png">
297<p>
298 for <code>n</code> odd and for <code>n</code> even <p class="formulaDsp">
299<img class="formulaDsp" alt="\[ w_i = w_{n-i-1} = \frac{2i+1}{n} \]" src="form_372.png">
300<p>
301 
302</div>
303</div><p>
304</div>
305<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:14 2009 for mixpp by&nbsp;
306<a href="http://www.doxygen.org/index.html">
307<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
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