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   5 <title>CMSIS DSP Software Library: DCT Type IV Functions</title>
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  45 <a href="#func-members">Functions</a> &#124;
  46 <a href="#var-members">Variables</a>  </div>
  47   <div class="headertitle">
  48 <h1>DCT Type IV Functions<br/>
  49 <small>
  50 [<a class="el" href="group__group_transforms.html">Transform Functions</a>]</small>
  51 </h1>  </div>
  52 </div>
  53 <div class="contents">
  54 <table class="memberdecls">
  55 <tr><td colspan="2"><h2><a name="func-members"></a>
  56 Functions</h2></td></tr>
  57 <tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gab094ad3bc6fa1b84e8b12a24e1850a06">arm_dct4_init_f32</a> (<a class="el" href="structarm__dct4__instance__f32.html">arm_dct4_instance_f32</a> *S, <a class="el" href="structarm__rfft__instance__f32.html">arm_rfft_instance_f32</a> *S_RFFT, <a class="el" href="structarm__cfft__radix4__instance__f32.html">arm_cfft_radix4_instance_f32</a> *S_CFFT, uint16_t N, uint16_t Nby2, <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> normalize)</td></tr>
  58 <tr><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gafd538d68886848bc090ec2b0d364cc81">arm_dct4_f32</a> (const <a class="el" href="structarm__dct4__instance__f32.html">arm_dct4_instance_f32</a> *S, <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *pState, <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *pInlineBuffer)</td></tr>
  59 <tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga631bb59c7c97c814ff7147ecba6a716a">arm_dct4_init_q31</a> (<a class="el" href="structarm__dct4__instance__q31.html">arm_dct4_instance_q31</a> *S, <a class="el" href="structarm__rfft__instance__q31.html">arm_rfft_instance_q31</a> *S_RFFT, <a class="el" href="structarm__cfft__radix4__instance__q31.html">arm_cfft_radix4_instance_q31</a> *S_CFFT, uint16_t N, uint16_t Nby2, <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> normalize)</td></tr>
  60 <tr><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gad04d0baab6ed081d8e8afe02538eb80b">arm_dct4_q31</a> (const <a class="el" href="structarm__dct4__instance__q31.html">arm_dct4_instance_q31</a> *S, <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *pState, <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *pInlineBuffer)</td></tr>
  61 <tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga966fd1b66a80873964533703ab5dc054">arm_dct4_init_q15</a> (<a class="el" href="structarm__dct4__instance__q15.html">arm_dct4_instance_q15</a> *S, <a class="el" href="structarm__rfft__instance__q15.html">arm_rfft_instance_q15</a> *S_RFFT, <a class="el" href="structarm__cfft__radix4__instance__q15.html">arm_cfft_radix4_instance_q15</a> *S_CFFT, uint16_t N, uint16_t Nby2, <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> normalize)</td></tr>
  62 <tr><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga114cb9635059f678df291fcc887aaf2b">arm_dct4_q15</a> (const <a class="el" href="structarm__dct4__instance__q15.html">arm_dct4_instance_q15</a> *S, <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> *pState, <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> *pInlineBuffer)</td></tr>
  63 <tr><td colspan="2"><h2><a name="var-members"></a>
  64 Variables</h2></td></tr>
  65 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gad00f29d896d64d6da7afbbb9d3e182a4">Weights_128</a> [256]</td></tr>
  66 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gaeb67b0be5b3c2139d660e02cedeed908">Weights_512</a> [1024]</td></tr>
  67 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gac3a2a00b3106dfcb5e0a582f50c65692">Weights_2048</a> [4096]</td></tr>
  68 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga16248ed86161ef97538011b49f13e8b7">cos_factors_128</a> [128]</td></tr>
  69 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga49fd288352ca5bb43f5cec52273b0d80">cos_factors_512</a> [512]</td></tr>
  70 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga1ba5306e0bc44730b40ab34cced45fd6">cos_factors_2048</a> [2048]</td></tr>
  71 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga02d7024538a87214296b01d83ba36b02">WeightsQ31_128</a> [256]</td></tr>
  72 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga31a8217a96f7d3171921e98398f31596">WeightsQ31_512</a> [1024]</td></tr>
  73 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga725b65c25a02b3cad329e18bb832f65e">WeightsQ31_2048</a> [4096]</td></tr>
  74 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gabb8ee2004a3520fd08388db637d43875">cos_factorsQ31_128</a> [128]</td></tr>
  75 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga3559569e603cb918911074be88523d0e">cos_factorsQ31_512</a> [512]</td></tr>
  76 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gaa15fc3fb058482defda371113cd12e74">cos_factorsQ31_2048</a> [2048]</td></tr>
  77 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga8e8f0253c5a4337bd90968838db6164d">WeightsQ15_128</a> [256]</td></tr>
  78 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga0492a1e2539ffb9d5276a357dab9dca1">WeightsQ15_512</a> [1024]</td></tr>
  79 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gab858d2072b29f338b5dabf5cde9aaf66">WeightsQ15_2048</a> [4096]</td></tr>
  80 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#ga373f2b52659505b0bb5066cd6c8a9041">cos_factorsQ15_128</a> [128]</td></tr>
  81 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gaf3a2b1f1c23720eed1c1fd380fcc43f9">cos_factorsQ15_512</a> [512]</td></tr>
  82 <tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___d_c_t4___i_d_c_t4.html#gafd1bd60aa573ba5ee349a05aaa32d915">cos_factorsQ15_2048</a> [2048]</td></tr>
  83 </table>
  84 <hr/><a name="_details"></a><h2>Detailed Description</h2>
  85 <p>Representation of signals by minimum number of values is important for storage and transmission. The possibility of large discontinuity between the beginning and end of a period of a signal in DFT can be avoided by extending the signal so that it is even-symmetric. Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the spectrum and is very widely used in signal and image coding applications. The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions. DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.</p>
  86 <p>DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal. Reordering of the input data makes the computation of DCT just a problem of computing the DFT of a real signal with a few additional operations. This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.</p>
  87 <p>DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used. DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing. DCT2 implementation can be described in the following steps:</p>
  88 <ul>
  89 <li>Re-ordering input</li>
  90 <li>Calculating Real FFT</li>
  91 <li>Multiplication of weights and Real FFT output and getting real part from the product.</li>
  92 </ul>
  93 <p>This process is explained by the block diagram below: </p>
  94 <div align="center">
  95 <img src="DCT4.gif" alt="DCT4.gif"/>
  96 <p><strong>Discrete Cosine Transform - type-IV</strong></p></div>
  97 <dl class="user"><dt><b>Algorithm: </b></dt><dd>The N-point type-IV DCT is defined as a real, linear transformation by the formula: <div align="center">
  98 <img src="DCT4Equation.gif" alt="DCT4Equation.gif"/>
  99 </div>
 100  where <code>k = 0,1,2,.....N-1</code> </dd></dl>
 101 <dl class="user"><dt><b></b></dt><dd>Its inverse is defined as follows: <div align="center">
 102 <img src="IDCT4Equation.gif" alt="IDCT4Equation.gif"/>
 103 </div>
 104  where <code>n = 0,1,2,.....N-1</code> </dd></dl>
 105 <dl class="user"><dt><b></b></dt><dd>The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N). The symmetry of the transform matrix indicates that the fast algorithms for the forward and inverse transform computation are identical. Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.</dd></dl>
 106 <dl class="user"><dt><b>Lengths supported by the transform: </b></dt><dd>As DCT4 internally uses Real FFT, it supports all the lengths supported by <a class="el" href="group___r_f_f_t___r_i_f_f_t.html#ga3df1766d230532bc068fc4ed69d0fcdc" title="Processing function for the floating-point RFFT/RIFFT.">arm_rfft_f32()</a>. The library provides separate functions for Q15, Q31, and floating-point data types. </dd></dl>
 107 <dl class="user"><dt><b>Instance Structure </b></dt><dd>The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure. A separate instance structure must be defined for each transform. There are separate instance structure declarations for each of the 3 supported data types.</dd></dl>
 108 <dl class="user"><dt><b>Initialization Functions </b></dt><dd>There is also an associated initialization function for each data type. The initialization function performs the following operations:<ul>
 109 <li>Sets the values of the internal structure fields.</li>
 110 <li>Initializes Real FFT as its process function is used internally in DCT4, by calling <a class="el" href="group___r_f_f_t___r_i_f_f_t.html#ga10717ee326bf50832ef1c25b85a23068" title="Initialization function for the floating-point RFFT/RIFFT.">arm_rfft_init_f32()</a>. </li>
 111 </ul>
 112 </dd></dl>
 113 <dl class="user"><dt><b></b></dt><dd>Use of the initialization function is optional. However, if the initialization function is used, then the instance structure cannot be placed into a const data section. To place an instance structure into a const data section, the instance structure must be manually initialized. Manually initialize the instance structure as follows: <pre>
 114 <a class="el" href="structarm__dct4__instance__f32.html" title="Instance structure for the floating-point DCT4/IDCT4 function.">arm_dct4_instance_f32</a> S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
 115 <a class="el" href="structarm__dct4__instance__q31.html" title="Instance structure for the Q31 DCT4/IDCT4 function.">arm_dct4_instance_q31</a> S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
 116 <a class="el" href="structarm__dct4__instance__q15.html" title="Instance structure for the Q15 DCT4/IDCT4 function.">arm_dct4_instance_q15</a> S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
 117  </pre> where <code>N</code> is the length of the DCT4; <code>Nby2</code> is half of the length of the DCT4; <code>normalize</code> is normalizing factor used and is equal to <code>sqrt(2/N)</code>; <code>pTwiddle</code> points to the twiddle factor table; <code>pCosFactor</code> points to the cosFactor table; <code>pRfft</code> points to the real FFT instance; <code>pCfft</code> points to the complex FFT instance; The CFFT and RFFT structures also needs to be initialized, refer to <a class="el" href="group___c_f_f_t___c_i_f_f_t.html#ga521f670cd9c571bc61aff9bec89f4c26" title="Processing function for the floating-point CFFT/CIFFT.">arm_cfft_radix4_f32()</a> and <a class="el" href="group___r_f_f_t___r_i_f_f_t.html#ga3df1766d230532bc068fc4ed69d0fcdc" title="Processing function for the floating-point RFFT/RIFFT.">arm_rfft_f32()</a> respectively for details regarding static initialization.</dd></dl>
 118 <dl class="user"><dt><b>Fixed-Point Behavior </b></dt><dd>Care must be taken when using the fixed-point versions of the DCT4 transform functions. In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. Refer to the function specific documentation below for usage guidelines. </dd></dl>
 119 <hr/><h2>Function Documentation</h2>
 120 <a class="anchor" id="gab094ad3bc6fa1b84e8b12a24e1850a06"></a><!-- doxytag: member="arm_dct4_init_f32.c::arm_dct4_init_f32" ref="gab094ad3bc6fa1b84e8b12a24e1850a06" args="(arm_dct4_instance_f32 *S, arm_rfft_instance_f32 *S_RFFT, arm_cfft_radix4_instance_f32 *S_CFFT, uint16_t N, uint16_t Nby2, float32_t normalize)" -->
 121 <div class="memitem">
 122 <div class="memproto">
 123       <table class="memname">
 124         <tr>
 125           <td class="memname"><a class="el" href="arm__math_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> arm_dct4_init_f32 </td>
 126           <td>(</td>
 127           <td class="paramtype"><a class="el" href="structarm__dct4__instance__f32.html">arm_dct4_instance_f32</a> *&#160;</td>
 128           <td class="paramname"> <em>S</em>, </td>
 129         </tr>
 130         <tr>
 131           <td class="paramkey"></td>
 132           <td></td>
 133           <td class="paramtype"><a class="el" href="structarm__rfft__instance__f32.html">arm_rfft_instance_f32</a> *&#160;</td>
 134           <td class="paramname"> <em>S_RFFT</em>, </td>
 135         </tr>
 136         <tr>
 137           <td class="paramkey"></td>
 138           <td></td>
 139           <td class="paramtype"><a class="el" href="structarm__cfft__radix4__instance__f32.html">arm_cfft_radix4_instance_f32</a> *&#160;</td>
 140           <td class="paramname"> <em>S_CFFT</em>, </td>
 141         </tr>
 142         <tr>
 143           <td class="paramkey"></td>
 144           <td></td>
 145           <td class="paramtype">uint16_t&#160;</td>
 146           <td class="paramname"> <em>N</em>, </td>
 147         </tr>
 148         <tr>
 149           <td class="paramkey"></td>
 150           <td></td>
 151           <td class="paramtype">uint16_t&#160;</td>
 152           <td class="paramname"> <em>Nby2</em>, </td>
 153         </tr>
 154         <tr>
 155           <td class="paramkey"></td>
 156           <td></td>
 157           <td class="paramtype"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td>
 158           <td class="paramname"> <em>normalize</em>&#160;</td>
 159         </tr>
 160         <tr>
 161           <td></td>
 162           <td>)</td>
 163           <td></td><td></td>
 164         </tr>
 165       </table>
 166 </div>
 167 <div class="memdoc">
 168
 169 <p>Initialization function for the floating-point DCT4/IDCT4. </p>
 170 <dl><dt><b>Parameters:</b></dt><dd>
 171   <table class="params">
 172     <tr><td class="paramdir">[in,out]</td><td class="paramname">*S</td><td>points to an instance of floating-point DCT4/IDCT4 structure. </td></tr>
 173     <tr><td class="paramdir">[in]</td><td class="paramname">*S_RFFT</td><td>points to an instance of floating-point RFFT/RIFFT structure. </td></tr>
 174     <tr><td class="paramdir">[in]</td><td class="paramname">*S_CFFT</td><td>points to an instance of floating-point CFFT/CIFFT structure. </td></tr>
 175     <tr><td class="paramdir">[in]</td><td class="paramname">N</td><td>length of the DCT4. </td></tr>
 176     <tr><td class="paramdir">[in]</td><td class="paramname">Nby2</td><td>half of the length of the DCT4. </td></tr>
 177     <tr><td class="paramdir">[in]</td><td class="paramname">normalize</td><td>normalizing factor. </td></tr>
 178   </table>
 179   </dd>
 180 </dl>
 181 <dl class="return"><dt><b>Returns:</b></dt><dd>arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length. </dd></dl>
 182 <dl class="user"><dt><b>Normalizing factor: </b></dt><dd>The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>. Floating-point normalizing factors are mentioned in the table below for different DCT sizes: <div align="center">
 183 <img src="dct4NormalizingF32Table.gif" alt="dct4NormalizingF32Table.gif"/>
 184 </div>
 185  </dd></dl>
 186
 187 <p>Definition at line <a class="el" href="arm__dct4__init__f32_8c_source.html#l04142">4142</a> of file <a class="el" href="arm__dct4__init__f32_8c_source.html">arm_dct4_init_f32.c</a>.</p>
 188
 189 </div>
 190 </div>
 191 <a class="anchor" id="gafd538d68886848bc090ec2b0d364cc81"></a><!-- doxytag: member="arm_dct4_f32.c::arm_dct4_f32" ref="gafd538d68886848bc090ec2b0d364cc81" args="(const arm_dct4_instance_f32 *S, float32_t *pState, float32_t *pInlineBuffer)" -->
 192 <div class="memitem">
 193 <div class="memproto">
 194       <table class="memname">
 195         <tr>
 196           <td class="memname">void arm_dct4_f32 </td>
 197           <td>(</td>
 198           <td class="paramtype">const <a class="el" href="structarm__dct4__instance__f32.html">arm_dct4_instance_f32</a> *&#160;</td>
 199           <td class="paramname"> <em>S</em>, </td>
 200         </tr>
 201         <tr>
 202           <td class="paramkey"></td>
 203           <td></td>
 204           <td class="paramtype"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *&#160;</td>
 205           <td class="paramname"> <em>pState</em>, </td>
 206         </tr>
 207         <tr>
 208           <td class="paramkey"></td>
 209           <td></td>
 210           <td class="paramtype"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *&#160;</td>
 211           <td class="paramname"> <em>pInlineBuffer</em>&#160;</td>
 212         </tr>
 213         <tr>
 214           <td></td>
 215           <td>)</td>
 216           <td></td><td></td>
 217         </tr>
 218       </table>
 219 </div>
 220 <div class="memdoc">
 221
 222 <p>Processing function for the floating-point DCT4/IDCT4. </p>
 223 <dl><dt><b>Parameters:</b></dt><dd>
 224   <table class="params">
 225     <tr><td class="paramdir">[in]</td><td class="paramname">*S</td><td>points to an instance of the floating-point DCT4/IDCT4 structure. </td></tr>
 226     <tr><td class="paramdir">[in]</td><td class="paramname">*pState</td><td>points to state buffer. </td></tr>
 227     <tr><td class="paramdir">[in,out]</td><td class="paramname">*pInlineBuffer</td><td>points to the in-place input and output buffer. </td></tr>
 228   </table>
 229   </dd>
 230 </dl>
 231 <dl class="return"><dt><b>Returns:</b></dt><dd>none. </dd></dl>
 232
 233 <p>Definition at line <a class="el" href="arm__dct4__f32_8c_source.html#l00126">126</a> of file <a class="el" href="arm__dct4__f32_8c_source.html">arm_dct4_f32.c</a>.</p>
 234
 235 </div>
 236 </div>
 237 <a class="anchor" id="ga631bb59c7c97c814ff7147ecba6a716a"></a><!-- doxytag: member="arm_dct4_init_q31.c::arm_dct4_init_q31" ref="ga631bb59c7c97c814ff7147ecba6a716a" args="(arm_dct4_instance_q31 *S, arm_rfft_instance_q31 *S_RFFT, arm_cfft_radix4_instance_q31 *S_CFFT, uint16_t N, uint16_t Nby2, q31_t normalize)" -->
 238 <div class="memitem">
 239 <div class="memproto">
 240       <table class="memname">
 241         <tr>
 242           <td class="memname"><a class="el" href="arm__math_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> arm_dct4_init_q31 </td>
 243           <td>(</td>
 244           <td class="paramtype"><a class="el" href="structarm__dct4__instance__q31.html">arm_dct4_instance_q31</a> *&#160;</td>
 245           <td class="paramname"> <em>S</em>, </td>
 246         </tr>
 247         <tr>
 248           <td class="paramkey"></td>
 249           <td></td>
 250           <td class="paramtype"><a class="el" href="structarm__rfft__instance__q31.html">arm_rfft_instance_q31</a> *&#160;</td>
 251           <td class="paramname"> <em>S_RFFT</em>, </td>
 252         </tr>
 253         <tr>
 254           <td class="paramkey"></td>
 255           <td></td>
 256           <td class="paramtype"><a class="el" href="structarm__cfft__radix4__instance__q31.html">arm_cfft_radix4_instance_q31</a> *&#160;</td>
 257           <td class="paramname"> <em>S_CFFT</em>, </td>
 258         </tr>
 259         <tr>
 260           <td class="paramkey"></td>
 261           <td></td>
 262           <td class="paramtype">uint16_t&#160;</td>
 263           <td class="paramname"> <em>N</em>, </td>
 264         </tr>
 265         <tr>
 266           <td class="paramkey"></td>
 267           <td></td>
 268           <td class="paramtype">uint16_t&#160;</td>
 269           <td class="paramname"> <em>Nby2</em>, </td>
 270         </tr>
 271         <tr>
 272           <td class="paramkey"></td>
 273           <td></td>
 274           <td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td>
 275           <td class="paramname"> <em>normalize</em>&#160;</td>
 276         </tr>
 277         <tr>
 278           <td></td>
 279           <td>)</td>
 280           <td></td><td></td>
 281         </tr>
 282       </table>
 283 </div>
 284 <div class="memdoc">
 285
 286 <p>Initialization function for the Q31 DCT4/IDCT4. </p>
 287 <dl><dt><b>Parameters:</b></dt><dd>
 288   <table class="params">
 289     <tr><td class="paramdir">[in,out]</td><td class="paramname">*S</td><td>points to an instance of Q31 DCT4/IDCT4 structure. </td></tr>
 290     <tr><td class="paramdir">[in]</td><td class="paramname">*S_RFFT</td><td>points to an instance of Q31 RFFT/RIFFT structure </td></tr>
 291     <tr><td class="paramdir">[in]</td><td class="paramname">*S_CFFT</td><td>points to an instance of Q31 CFFT/CIFFT structure </td></tr>
 292     <tr><td class="paramdir">[in]</td><td class="paramname">N</td><td>length of the DCT4. </td></tr>
 293     <tr><td class="paramdir">[in]</td><td class="paramname">Nby2</td><td>half of the length of the DCT4. </td></tr>
 294     <tr><td class="paramdir">[in]</td><td class="paramname">normalize</td><td>normalizing factor. </td></tr>
 295   </table>
 296   </dd>
 297 </dl>
 298 <dl class="return"><dt><b>Returns:</b></dt><dd>arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length. </dd></dl>
 299 <dl class="user"><dt><b>Normalizing factor: </b></dt><dd>The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>. Normalizing factors in 1.31 format are mentioned in the table below for different DCT sizes: <div align="center">
 300 <img src="dct4NormalizingQ31Table.gif" alt="dct4NormalizingQ31Table.gif"/>
 301 </div>
 302  </dd></dl>
 303
 304 <p>Definition at line <a class="el" href="arm__dct4__init__q31_8c_source.html#l02133">2133</a> of file <a class="el" href="arm__dct4__init__q31_8c_source.html">arm_dct4_init_q31.c</a>.</p>
 305
 306 </div>
 307 </div>
 308 <a class="anchor" id="gad04d0baab6ed081d8e8afe02538eb80b"></a><!-- doxytag: member="arm_dct4_q31.c::arm_dct4_q31" ref="gad04d0baab6ed081d8e8afe02538eb80b" args="(const arm_dct4_instance_q31 *S, q31_t *pState, q31_t *pInlineBuffer)" -->
 309 <div class="memitem">
 310 <div class="memproto">
 311       <table class="memname">
 312         <tr>
 313           <td class="memname">void arm_dct4_q31 </td>
 314           <td>(</td>
 315           <td class="paramtype">const <a class="el" href="structarm__dct4__instance__q31.html">arm_dct4_instance_q31</a> *&#160;</td>
 316           <td class="paramname"> <em>S</em>, </td>
 317         </tr>
 318         <tr>
 319           <td class="paramkey"></td>
 320           <td></td>
 321           <td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *&#160;</td>
 322           <td class="paramname"> <em>pState</em>, </td>
 323         </tr>
 324         <tr>
 325           <td class="paramkey"></td>
 326           <td></td>
 327           <td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *&#160;</td>
 328           <td class="paramname"> <em>pInlineBuffer</em>&#160;</td>
 329         </tr>
 330         <tr>
 331           <td></td>
 332           <td>)</td>
 333           <td></td><td></td>
 334         </tr>
 335       </table>
 336 </div>
 337 <div class="memdoc">
 338
 339 <p>Processing function for the Q31 DCT4/IDCT4. </p>
 340 <dl><dt><b>Parameters:</b></dt><dd>
 341   <table class="params">
 342     <tr><td class="paramdir">[in]</td><td class="paramname">*S</td><td>points to an instance of the Q31 DCT4 structure. </td></tr>
 343     <tr><td class="paramdir">[in]</td><td class="paramname">*pState</td><td>points to state buffer. </td></tr>
 344     <tr><td class="paramdir">[in,out]</td><td class="paramname">*pInlineBuffer</td><td>points to the in-place input and output buffer. </td></tr>
 345   </table>
 346   </dd>
 347 </dl>
 348 <dl class="return"><dt><b>Returns:</b></dt><dd>none. </dd></dl>
 349 <dl class="user"><dt><b>Input an output formats: </b></dt><dd>Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process, as the conversion from DCT2 to DCT4 involves one subtraction. Internally inputs are downscaled in the RFFT process function to avoid overflows. Number of bits downscaled, depends on the size of the transform. The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:</dd></dl>
 350 <div align="center">
 351 <img src="dct4FormatsQ31Table.gif" alt="dct4FormatsQ31Table.gif"/>
 352 </div>
 353
 354 <p>Definition at line <a class="el" href="arm__dct4__q31_8c_source.html#l00053">53</a> of file <a class="el" href="arm__dct4__q31_8c_source.html">arm_dct4_q31.c</a>.</p>
 355
 356 </div>
 357 </div>
 358 <a class="anchor" id="ga966fd1b66a80873964533703ab5dc054"></a><!-- doxytag: member="arm_dct4_init_q15.c::arm_dct4_init_q15" ref="ga966fd1b66a80873964533703ab5dc054" args="(arm_dct4_instance_q15 *S, arm_rfft_instance_q15 *S_RFFT, arm_cfft_radix4_instance_q15 *S_CFFT, uint16_t N, uint16_t Nby2, q15_t normalize)" -->
 359 <div class="memitem">
 360 <div class="memproto">
 361       <table class="memname">
 362         <tr>
 363           <td class="memname"><a class="el" href="arm__math_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> arm_dct4_init_q15 </td>
 364           <td>(</td>
 365           <td class="paramtype"><a class="el" href="structarm__dct4__instance__q15.html">arm_dct4_instance_q15</a> *&#160;</td>
 366           <td class="paramname"> <em>S</em>, </td>
 367         </tr>
 368         <tr>
 369           <td class="paramkey"></td>
 370           <td></td>
 371           <td class="paramtype"><a class="el" href="structarm__rfft__instance__q15.html">arm_rfft_instance_q15</a> *&#160;</td>
 372           <td class="paramname"> <em>S_RFFT</em>, </td>
 373         </tr>
 374         <tr>
 375           <td class="paramkey"></td>
 376           <td></td>
 377           <td class="paramtype"><a class="el" href="structarm__cfft__radix4__instance__q15.html">arm_cfft_radix4_instance_q15</a> *&#160;</td>
 378           <td class="paramname"> <em>S_CFFT</em>, </td>
 379         </tr>
 380         <tr>
 381           <td class="paramkey"></td>
 382           <td></td>
 383           <td class="paramtype">uint16_t&#160;</td>
 384           <td class="paramname"> <em>N</em>, </td>
 385         </tr>
 386         <tr>
 387           <td class="paramkey"></td>
 388           <td></td>
 389           <td class="paramtype">uint16_t&#160;</td>
 390           <td class="paramname"> <em>Nby2</em>, </td>
 391         </tr>
 392         <tr>
 393           <td class="paramkey"></td>
 394           <td></td>
 395           <td class="paramtype"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td>
 396           <td class="paramname"> <em>normalize</em>&#160;</td>
 397         </tr>
 398         <tr>
 399           <td></td>
 400           <td>)</td>
 401           <td></td><td></td>
 402         </tr>
 403       </table>
 404 </div>
 405 <div class="memdoc">
 406
 407 <p>Initialization function for the Q15 DCT4/IDCT4. </p>
 408 <dl><dt><b>Parameters:</b></dt><dd>
 409   <table class="params">
 410     <tr><td class="paramdir">[in,out]</td><td class="paramname">*S</td><td>points to an instance of Q15 DCT4/IDCT4 structure. </td></tr>
 411     <tr><td class="paramdir">[in]</td><td class="paramname">*S_RFFT</td><td>points to an instance of Q15 RFFT/RIFFT structure. </td></tr>
 412     <tr><td class="paramdir">[in]</td><td class="paramname">*S_CFFT</td><td>points to an instance of Q15 CFFT/CIFFT structure. </td></tr>
 413     <tr><td class="paramdir">[in]</td><td class="paramname">N</td><td>length of the DCT4. </td></tr>
 414     <tr><td class="paramdir">[in]</td><td class="paramname">Nby2</td><td>half of the length of the DCT4. </td></tr>
 415     <tr><td class="paramdir">[in]</td><td class="paramname">normalize</td><td>normalizing factor. </td></tr>
 416   </table>
 417   </dd>
 418 </dl>
 419 <dl class="return"><dt><b>Returns:</b></dt><dd>arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length. </dd></dl>
 420 <dl class="user"><dt><b>Normalizing factor: </b></dt><dd>The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>. Normalizing factors in 1.15 format are mentioned in the table below for different DCT sizes: <div align="center">
 421 <img src="dct4NormalizingQ15Table.gif" alt="dct4NormalizingQ15Table.gif"/>
 422 </div>
 423  </dd></dl>
 424
 425 <p>Definition at line <a class="el" href="arm__dct4__init__q15_8c_source.html#l01125">1125</a> of file <a class="el" href="arm__dct4__init__q15_8c_source.html">arm_dct4_init_q15.c</a>.</p>
 426
 427 </div>
 428 </div>
 429 <a class="anchor" id="ga114cb9635059f678df291fcc887aaf2b"></a><!-- doxytag: member="arm_dct4_q15.c::arm_dct4_q15" ref="ga114cb9635059f678df291fcc887aaf2b" args="(const arm_dct4_instance_q15 *S, q15_t *pState, q15_t *pInlineBuffer)" -->
 430 <div class="memitem">
 431 <div class="memproto">
 432       <table class="memname">
 433         <tr>
 434           <td class="memname">void arm_dct4_q15 </td>
 435           <td>(</td>
 436           <td class="paramtype">const <a class="el" href="structarm__dct4__instance__q15.html">arm_dct4_instance_q15</a> *&#160;</td>
 437           <td class="paramname"> <em>S</em>, </td>
 438         </tr>
 439         <tr>
 440           <td class="paramkey"></td>
 441           <td></td>
 442           <td class="paramtype"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> *&#160;</td>
 443           <td class="paramname"> <em>pState</em>, </td>
 444         </tr>
 445         <tr>
 446           <td class="paramkey"></td>
 447           <td></td>
 448           <td class="paramtype"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> *&#160;</td>
 449           <td class="paramname"> <em>pInlineBuffer</em>&#160;</td>
 450         </tr>
 451         <tr>
 452           <td></td>
 453           <td>)</td>
 454           <td></td><td></td>
 455         </tr>
 456       </table>
 457 </div>
 458 <div class="memdoc">
 459
 460 <p>Processing function for the Q15 DCT4/IDCT4. </p>
 461 <dl><dt><b>Parameters:</b></dt><dd>
 462   <table class="params">
 463     <tr><td class="paramdir">[in]</td><td class="paramname">*S</td><td>points to an instance of the Q15 DCT4 structure. </td></tr>
 464     <tr><td class="paramdir">[in]</td><td class="paramname">*pState</td><td>points to state buffer. </td></tr>
 465     <tr><td class="paramdir">[in,out]</td><td class="paramname">*pInlineBuffer</td><td>points to the in-place input and output buffer. </td></tr>
 466   </table>
 467   </dd>
 468 </dl>
 469 <dl class="return"><dt><b>Returns:</b></dt><dd>none.</dd></dl>
 470 <dl class="user"><dt><b>Input an output formats: </b></dt><dd>Internally inputs are downscaled in the RFFT process function to avoid overflows. Number of bits downscaled, depends on the size of the transform. The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:</dd></dl>
 471 <div align="center">
 472 <img src="dct4FormatsQ15Table.gif" alt="dct4FormatsQ15Table.gif"/>
 473 </div>
 474
 475 <p>Definition at line <a class="el" href="arm__dct4__q15_8c_source.html#l00052">52</a> of file <a class="el" href="arm__dct4__q15_8c_source.html">arm_dct4_q15.c</a>.</p>
 476
 477 </div>
 478 </div>
 479 <hr/><h2>Variable Documentation</h2>
 480 <a class="anchor" id="gad00f29d896d64d6da7afbbb9d3e182a4"></a><!-- doxytag: member="arm_dct4_init_f32.c::Weights_128" ref="gad00f29d896d64d6da7afbbb9d3e182a4" args="[256]" -->
 481 <div class="memitem">
 482 <div class="memproto">
 483       <table class="memname">
 484         <tr>
 485           <td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#gad00f29d896d64d6da7afbbb9d3e182a4">Weights_128</a>[256]<code> [static]</code></td>
 486         </tr>
 487       </table>
 488 </div>
 489 <div class="memdoc">
 490 <dl class="user"><dt><b></b></dt><dd>Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre> </dd></dl>
 491 <dl class="user"><dt><b></b></dt><dd>C command to generate the table <pre>
 492  for(i = 0; i&lt; N; i++)
 493  {
 494     weights[2*i]= cos(i*c);
 495     weights[(2*i)+1]= -sin(i * c);
 496  } </pre> </dd></dl>
 497 <dl class="user"><dt><b></b></dt><dd>Where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code> </dd></dl>
 498 <dl class="user"><dt><b></b></dt><dd>In the tables below the real and imaginary values are placed alternatively, hence the array length is <code>2*N</code>. </dd></dl>
 499
 500 <p>Definition at line <a class="el" href="arm__dct4__init__f32_8c_source.html#l00064">64</a> of file <a class="el" href="arm__dct4__init__f32_8c_source.html">arm_dct4_init_f32.c</a>.</p>
 501
 502 </div>
 503 </div>
 504 <a class="anchor" id="gaeb67b0be5b3c2139d660e02cedeed908"></a><!-- doxytag: member="arm_dct4_init_f32.c::Weights_512" ref="gaeb67b0be5b3c2139d660e02cedeed908" args="[1024]" -->
 505 <div class="memitem">
 506 <div class="memproto">
 507       <table class="memname">
 508         <tr>
 509           <td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#gaeb67b0be5b3c2139d660e02cedeed908">Weights_512</a>[1024]<code> [static]</code></td>
 510         </tr>
 511       </table>
 512 </div>
 513 <div class="memdoc">
 514
 515 <p>Definition at line <a class="el" href="arm__dct4__init__f32_8c_source.html#l00195">195</a> of file <a class="el" href="arm__dct4__init__f32_8c_source.html">arm_dct4_init_f32.c</a>.</p>
 516
 517 </div>
 518 </div>
 519 <a class="anchor" id="gac3a2a00b3106dfcb5e0a582f50c65692"></a><!-- doxytag: member="arm_dct4_init_f32.c::Weights_2048" ref="gac3a2a00b3106dfcb5e0a582f50c65692" args="[4096]" -->
 520 <div class="memitem">
 521 <div class="memproto">
 522       <table class="memname">
 523         <tr>
 524           <td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#gac3a2a00b3106dfcb5e0a582f50c65692">Weights_2048</a>[4096]<code> [static]</code></td>
 525         </tr>
 526       </table>
 527 </div>
 528 <div class="memdoc">
 529
 530 <p>Definition at line <a class="el" href="arm__dct4__init__f32_8c_source.html#l00710">710</a> of file <a class="el" href="arm__dct4__init__f32_8c_source.html">arm_dct4_init_f32.c</a>.</p>
 531
 532 </div>
 533 </div>
 534 <a class="anchor" id="ga16248ed86161ef97538011b49f13e8b7"></a><!-- doxytag: member="arm_dct4_init_f32.c::cos_factors_128" ref="ga16248ed86161ef97538011b49f13e8b7" args="[128]" -->
 535 <div class="memitem">
 536 <div class="memproto">
 537       <table class="memname">
 538         <tr>
 539           <td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga16248ed86161ef97538011b49f13e8b7">cos_factors_128</a>[128]<code> [static]</code></td>
 540         </tr>
 541       </table>
 542 </div>
 543 <div class="memdoc">
 544 <dl class="user"><dt><b></b></dt><dd>cosFactor tables are generated using the formula : <pre>cos_factors[n] = 2 * cos((2n+1)*pi/(4*N))</pre> </dd></dl>
 545 <dl class="user"><dt><b></b></dt><dd>C command to generate the table </dd></dl>
 546 <dl class="user"><dt><b></b></dt><dd><pre> for(i = 0; i&lt; N; i++)
 547  {
 548     cos_factors[i]= 2 * cos((2*i+1)*c/2);
 549  } </pre> </dd></dl>
 550 <dl class="user"><dt><b></b></dt><dd>where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code> </dd></dl>
 551
 552 <p>Definition at line <a class="el" href="arm__dct4__init__f32_8c_source.html#l02774">2774</a> of file <a class="el" href="arm__dct4__init__f32_8c_source.html">arm_dct4_init_f32.c</a>.</p>
 553
 554 </div>
 555 </div>
 556 <a class="anchor" id="ga49fd288352ca5bb43f5cec52273b0d80"></a><!-- doxytag: member="arm_dct4_init_f32.c::cos_factors_512" ref="ga49fd288352ca5bb43f5cec52273b0d80" args="[512]" -->
 557 <div class="memitem">
 558 <div class="memproto">
 559       <table class="memname">
 560         <tr>
 561           <td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga49fd288352ca5bb43f5cec52273b0d80">cos_factors_512</a>[512]<code> [static]</code></td>
 562         </tr>
 563       </table>
 564 </div>
 565 <div class="memdoc">
 566
 567 <p>Definition at line <a class="el" href="arm__dct4__init__f32_8c_source.html#l02841">2841</a> of file <a class="el" href="arm__dct4__init__f32_8c_source.html">arm_dct4_init_f32.c</a>.</p>
 568
 569 </div>
 570 </div>
 571 <a class="anchor" id="ga1ba5306e0bc44730b40ab34cced45fd6"></a><!-- doxytag: member="arm_dct4_init_f32.c::cos_factors_2048" ref="ga1ba5306e0bc44730b40ab34cced45fd6" args="[2048]" -->
 572 <div class="memitem">
 573 <div class="memproto">
 574       <table class="memname">
 575         <tr>
 576           <td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga1ba5306e0bc44730b40ab34cced45fd6">cos_factors_2048</a>[2048]<code> [static]</code></td>
 577         </tr>
 578       </table>
 579 </div>
 580 <div class="memdoc">
 581
 582 <p>Definition at line <a class="el" href="arm__dct4__init__f32_8c_source.html#l03100">3100</a> of file <a class="el" href="arm__dct4__init__f32_8c_source.html">arm_dct4_init_f32.c</a>.</p>
 583
 584 </div>
 585 </div>
 586 <a class="anchor" id="ga02d7024538a87214296b01d83ba36b02"></a><!-- doxytag: member="arm_dct4_init_q31.c::WeightsQ31_128" ref="ga02d7024538a87214296b01d83ba36b02" args="[256]" -->
 587 <div class="memitem">
 588 <div class="memproto">
 589       <table class="memname">
 590         <tr>
 591           <td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga02d7024538a87214296b01d83ba36b02">WeightsQ31_128</a>[256]<code> [static]</code></td>
 592         </tr>
 593       </table>
 594 </div>
 595 <div class="memdoc">
 596 <dl class="user"><dt><b></b></dt><dd>Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre> </dd></dl>
 597 <dl class="user"><dt><b></b></dt><dd>C command to generate the table <pre>
 598  for(i = 0; i&lt; N; i++)
 599  {
 600    weights[2*i]= cos(i*c);
 601    weights[(2*i)+1]= -sin(i * c);
 602  } </pre> </dd></dl>
 603 <dl class="user"><dt><b></b></dt><dd>where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code> </dd></dl>
 604 <dl class="user"><dt><b></b></dt><dd>Convert the output to q31 format by multiplying with 2^31 and saturated if required. </dd></dl>
 605 <dl class="user"><dt><b></b></dt><dd>In the tables below the real and imaginary values are placed alternatively, hence the array length is <code>2*N</code>. </dd></dl>
 606
 607 <p>Definition at line <a class="el" href="arm__dct4__init__q31_8c_source.html#l00066">66</a> of file <a class="el" href="arm__dct4__init__q31_8c_source.html">arm_dct4_init_q31.c</a>.</p>
 608
 609 </div>
 610 </div>
 611 <a class="anchor" id="ga31a8217a96f7d3171921e98398f31596"></a><!-- doxytag: member="arm_dct4_init_q31.c::WeightsQ31_512" ref="ga31a8217a96f7d3171921e98398f31596" args="[1024]" -->
 612 <div class="memitem">
 613 <div class="memproto">
 614       <table class="memname">
 615         <tr>
 616           <td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga31a8217a96f7d3171921e98398f31596">WeightsQ31_512</a>[1024]<code> [static]</code></td>
 617         </tr>
 618       </table>
 619 </div>
 620 <div class="memdoc">
 621
 622 <p>Definition at line <a class="el" href="arm__dct4__init__q31_8c_source.html#l00133">133</a> of file <a class="el" href="arm__dct4__init__q31_8c_source.html">arm_dct4_init_q31.c</a>.</p>
 623
 624 </div>
 625 </div>
 626 <a class="anchor" id="ga725b65c25a02b3cad329e18bb832f65e"></a><!-- doxytag: member="arm_dct4_init_q31.c::WeightsQ31_2048" ref="ga725b65c25a02b3cad329e18bb832f65e" args="[4096]" -->
 627 <div class="memitem">
 628 <div class="memproto">
 629       <table class="memname">
 630         <tr>
 631           <td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga725b65c25a02b3cad329e18bb832f65e">WeightsQ31_2048</a>[4096]<code> [static]</code></td>
 632         </tr>
 633       </table>
 634 </div>
 635 <div class="memdoc">
 636
 637 <p>Definition at line <a class="el" href="arm__dct4__init__q31_8c_source.html#l00392">392</a> of file <a class="el" href="arm__dct4__init__q31_8c_source.html">arm_dct4_init_q31.c</a>.</p>
 638
 639 </div>
 640 </div>
 641 <a class="anchor" id="gabb8ee2004a3520fd08388db637d43875"></a><!-- doxytag: member="arm_dct4_init_q31.c::cos_factorsQ31_128" ref="gabb8ee2004a3520fd08388db637d43875" args="[128]" -->
 642 <div class="memitem">
 643 <div class="memproto">
 644       <table class="memname">
 645         <tr>
 646           <td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#gabb8ee2004a3520fd08388db637d43875">cos_factorsQ31_128</a>[128]<code> [static]</code></td>
 647         </tr>
 648       </table>
 649 </div>
 650 <div class="memdoc">
 651 <dl class="user"><dt><b></b></dt><dd>cosFactor tables are generated using the formula : <pre>cos_factors[n] = 2 * cos((2n+1)*pi/(4*N))</pre> </dd></dl>
 652 <dl class="user"><dt><b></b></dt><dd>C command to generate the table <pre>
 653  for(i = 0; i&lt; N; i++)
 654  {
 655    cos_factors[i]= 2 * cos((2*i+1)*c/2);
 656  } </pre> </dd></dl>
 657 <dl class="user"><dt><b></b></dt><dd>where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code> </dd></dl>
 658 <dl class="user"><dt><b></b></dt><dd>Then converted to q31 format by multiplying with 2^31 and saturated if required. </dd></dl>
 659
 660 <p>Definition at line <a class="el" href="arm__dct4__init__q31_8c_source.html#l01436">1436</a> of file <a class="el" href="arm__dct4__init__q31_8c_source.html">arm_dct4_init_q31.c</a>.</p>
 661
 662 </div>
 663 </div>
 664 <a class="anchor" id="ga3559569e603cb918911074be88523d0e"></a><!-- doxytag: member="arm_dct4_init_q31.c::cos_factorsQ31_512" ref="ga3559569e603cb918911074be88523d0e" args="[512]" -->
 665 <div class="memitem">
 666 <div class="memproto">
 667       <table class="memname">
 668         <tr>
 669           <td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga3559569e603cb918911074be88523d0e">cos_factorsQ31_512</a>[512]<code> [static]</code></td>
 670         </tr>
 671       </table>
 672 </div>
 673 <div class="memdoc">
 674
 675 <p>Definition at line <a class="el" href="arm__dct4__init__q31_8c_source.html#l01471">1471</a> of file <a class="el" href="arm__dct4__init__q31_8c_source.html">arm_dct4_init_q31.c</a>.</p>
 676
 677 </div>
 678 </div>
 679 <a class="anchor" id="gaa15fc3fb058482defda371113cd12e74"></a><!-- doxytag: member="arm_dct4_init_q31.c::cos_factorsQ31_2048" ref="gaa15fc3fb058482defda371113cd12e74" args="[2048]" -->
 680 <div class="memitem">
 681 <div class="memproto">
 682       <table class="memname">
 683         <tr>
 684           <td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#gaa15fc3fb058482defda371113cd12e74">cos_factorsQ31_2048</a>[2048]<code> [static]</code></td>
 685         </tr>
 686       </table>
 687 </div>
 688 <div class="memdoc">
 689
 690 <p>Definition at line <a class="el" href="arm__dct4__init__q31_8c_source.html#l01602">1602</a> of file <a class="el" href="arm__dct4__init__q31_8c_source.html">arm_dct4_init_q31.c</a>.</p>
 691
 692 </div>
 693 </div>
 694 <a class="anchor" id="ga8e8f0253c5a4337bd90968838db6164d"></a><!-- doxytag: member="arm_dct4_init_q15.c::WeightsQ15_128" ref="ga8e8f0253c5a4337bd90968838db6164d" args="[256]" -->
 695 <div class="memitem">
 696 <div class="memproto">
 697       <table class="memname">
 698         <tr>
 699           <td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga8e8f0253c5a4337bd90968838db6164d">WeightsQ15_128</a>[256]<code> [static]</code></td>
 700         </tr>
 701       </table>
 702 </div>
 703 <div class="memdoc">
 704 <dl class="user"><dt><b></b></dt><dd>Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre> </dd></dl>
 705 <dl class="user"><dt><b></b></dt><dd>C command to generate the table <pre>
 706  for(i = 0; i&lt; N; i++)
 707  {
 708    weights[2*i]= cos(i*c);
 709    weights[(2*i)+1]= -sin(i * c);
 710  } </pre> </dd></dl>
 711 <dl class="user"><dt><b></b></dt><dd>where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code> </dd></dl>
 712 <dl class="user"><dt><b></b></dt><dd>Converted the output to q15 format by multiplying with 2^31 and saturated if required. </dd></dl>
 713 <dl class="user"><dt><b></b></dt><dd>In the tables below the real and imaginary values are placed alternatively, hence the array length is <code>2*N</code>. </dd></dl>
 714
 715 <p>Definition at line <a class="el" href="arm__dct4__init__q15_8c_source.html#l00066">66</a> of file <a class="el" href="arm__dct4__init__q15_8c_source.html">arm_dct4_init_q15.c</a>.</p>
 716
 717 </div>
 718 </div>
 719 <a class="anchor" id="ga0492a1e2539ffb9d5276a357dab9dca1"></a><!-- doxytag: member="arm_dct4_init_q15.c::WeightsQ15_512" ref="ga0492a1e2539ffb9d5276a357dab9dca1" args="[1024]" -->
 720 <div class="memitem">
 721 <div class="memproto">
 722       <table class="memname">
 723         <tr>
 724           <td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga0492a1e2539ffb9d5276a357dab9dca1">WeightsQ15_512</a>[1024]<code> [static]</code></td>
 725         </tr>
 726       </table>
 727 </div>
 728 <div class="memdoc">
 729
 730 <p>Definition at line <a class="el" href="arm__dct4__init__q15_8c_source.html#l00101">101</a> of file <a class="el" href="arm__dct4__init__q15_8c_source.html">arm_dct4_init_q15.c</a>.</p>
 731
 732 </div>
 733 </div>
 734 <a class="anchor" id="gab858d2072b29f338b5dabf5cde9aaf66"></a><!-- doxytag: member="arm_dct4_init_q15.c::WeightsQ15_2048" ref="gab858d2072b29f338b5dabf5cde9aaf66" args="[4096]" -->
 735 <div class="memitem">
 736 <div class="memproto">
 737       <table class="memname">
 738         <tr>
 739           <td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#gab858d2072b29f338b5dabf5cde9aaf66">WeightsQ15_2048</a>[4096]<code> [static]</code></td>
 740         </tr>
 741       </table>
 742 </div>
 743 <div class="memdoc">
 744
 745 <p>Definition at line <a class="el" href="arm__dct4__init__q15_8c_source.html#l00232">232</a> of file <a class="el" href="arm__dct4__init__q15_8c_source.html">arm_dct4_init_q15.c</a>.</p>
 746
 747 </div>
 748 </div>
 749 <a class="anchor" id="ga373f2b52659505b0bb5066cd6c8a9041"></a><!-- doxytag: member="arm_dct4_init_q15.c::cos_factorsQ15_128" ref="ga373f2b52659505b0bb5066cd6c8a9041" args="[128]" -->
 750 <div class="memitem">
 751 <div class="memproto">
 752       <table class="memname">
 753         <tr>
 754           <td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#ga373f2b52659505b0bb5066cd6c8a9041">cos_factorsQ15_128</a>[128]<code> [static]</code></td>
 755         </tr>
 756       </table>
 757 </div>
 758 <div class="memdoc">
 759 <b>Initial value:</b><div class="fragment"><pre class="fragment"> {
 760   0x7fff, 0x7ffa, 0x7ff0, 0x7fe1, 0x7fce, 0x7fb5, 0x7f97, 0x7f75,
 761   0x7f4d, 0x7f21, 0x7ef0, 0x7eba, 0x7e7f, 0x7e3f, 0x7dfa, 0x7db0,
 762   0x7d62, 0x7d0f, 0x7cb7, 0x7c5a, 0x7bf8, 0x7b92, 0x7b26, 0x7ab6,
 763   0x7a42, 0x79c8, 0x794a, 0x78c7, 0x7840, 0x77b4, 0x7723, 0x768e,
 764   0x75f4, 0x7555, 0x74b2, 0x740b, 0x735f, 0x72af, 0x71fa, 0x7141,
 765   0x7083, 0x6fc1, 0x6efb, 0x6e30, 0x6d62, 0x6c8f, 0x6bb8, 0x6adc,
 766   0x69fd, 0x6919, 0x6832, 0x6746, 0x6657, 0x6563, 0x646c, 0x6371,
 767   0x6271, 0x616f, 0x6068, 0x5f5e, 0x5e50, 0x5d3e, 0x5c29, 0x5b10,
 768   0x59f3, 0x58d4, 0x57b0, 0x568a, 0x5560, 0x5433, 0x5302, 0x51ce,
 769   0x5097, 0x4f5e, 0x4e21, 0x4ce1, 0x4b9e, 0x4a58, 0x490f, 0x47c3,
 770   0x4675, 0x4524, 0x43d0, 0x427a, 0x4121, 0x3fc5, 0x3e68, 0x3d07,
 771   0x3ba5, 0x3a40, 0x38d8, 0x376f, 0x3604, 0x3496, 0x3326, 0x31b5,
 772   0x3041, 0x2ecc, 0x2d55, 0x2bdc, 0x2a61, 0x28e5, 0x2767, 0x25e8,
 773   0x2467, 0x22e5, 0x2161, 0x1fdc, 0x1e56, 0x1ccf, 0x1b47, 0x19bd,
 774   0x1833, 0x16a8, 0x151b, 0x138e, 0x1201, 0x1072, 0xee3, 0xd53,
 775   0xbc3, 0xa33, 0x8a2, 0x710, 0x57f, 0x3ed, 0x25b, 0xc9
 776 }
 777 </pre></div><dl class="user"><dt><b></b></dt><dd>cosFactor tables are generated using the formula : <pre> cos_factors[n] = 2 * cos((2n+1)*pi/(4*N)) </pre> </dd></dl>
 778 <dl class="user"><dt><b></b></dt><dd>C command to generate the table <pre>
 779  for(i = 0; i&lt; N; i++)
 780  {
 781    cos_factors[i]= 2 * cos((2*i+1)*c/2);
 782  } </pre> </dd></dl>
 783 <dl class="user"><dt><b></b></dt><dd>where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code> </dd></dl>
 784 <dl class="user"><dt><b></b></dt><dd>Then converted to q15 format by multiplying with 2^31 and saturated if required. </dd></dl>
 785
 786 <p>Definition at line <a class="el" href="arm__dct4__init__q15_8c_source.html#l00764">764</a> of file <a class="el" href="arm__dct4__init__q15_8c_source.html">arm_dct4_init_q15.c</a>.</p>
 787
 788 </div>
 789 </div>
 790 <a class="anchor" id="gaf3a2b1f1c23720eed1c1fd380fcc43f9"></a><!-- doxytag: member="arm_dct4_init_q15.c::cos_factorsQ15_512" ref="gaf3a2b1f1c23720eed1c1fd380fcc43f9" args="[512]" -->
 791 <div class="memitem">
 792 <div class="memproto">
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 795           <td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#gaf3a2b1f1c23720eed1c1fd380fcc43f9">cos_factorsQ15_512</a>[512]<code> [static]</code></td>
 796         </tr>
 797       </table>
 798 </div>
 799 <div class="memdoc">
 800
 801 <p>Definition at line <a class="el" href="arm__dct4__init__q15_8c_source.html#l00783">783</a> of file <a class="el" href="arm__dct4__init__q15_8c_source.html">arm_dct4_init_q15.c</a>.</p>
 802
 803 </div>
 804 </div>
 805 <a class="anchor" id="gafd1bd60aa573ba5ee349a05aaa32d915"></a><!-- doxytag: member="arm_dct4_init_q15.c::cos_factorsQ15_2048" ref="gafd1bd60aa573ba5ee349a05aaa32d915" args="[2048]" -->
 806 <div class="memitem">
 807 <div class="memproto">
 808       <table class="memname">
 809         <tr>
 810           <td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group___d_c_t4___i_d_c_t4.html#gafd1bd60aa573ba5ee349a05aaa32d915">cos_factorsQ15_2048</a>[2048]<code> [static]</code></td>
 811         </tr>
 812       </table>
 813 </div>
 814 <div class="memdoc">
 815
 816 <p>Definition at line <a class="el" href="arm__dct4__init__q15_8c_source.html#l00850">850</a> of file <a class="el" href="arm__dct4__init__q15_8c_source.html">arm_dct4_init_q15.c</a>.</p>
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 835 <hr class="footer"/><address class="footer"><small>Generated on Fri Jul 15 2011 13:16:21 for CMSIS DSP Software Library by&#160;
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