<dt>Global <aclass="el"href="group__ComplexFFT.html#gaad799b60792f7ffa0ff971b5d9827eb9">arm_cfft_radix2_f16</a> (const <aclass="el"href="structarm__cfft__radix2__instance__f16.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix2_instance_f16</a> *S, float16_t *pSrc)</dt>
<dd><aclass="anchor"id="_deprecated000002"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future </dd>
<dd><aclass="anchor"id="_deprecated000004"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga9fadd650b802f612ae558ddaab789a6d">arm_cfft_radix2_f32</a> (const <aclass="el"href="structarm__cfft__radix2__instance__f32.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix2_instance_f32</a> *S, float32_t *pSrc)</dt>
<dd><aclass="anchor"id="_deprecated000003"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future </dd>
<dd><aclass="anchor"id="_deprecated000005"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga76de02a40b34e5ff8c20886d34fdcd71">arm_cfft_radix2_init_f16</a> (<aclass="el"href="structarm__cfft__radix2__instance__f16.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix2_instance_f16</a> *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000004"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000006"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#gac9565e6bc7229577ecf5e090313cafd7">arm_cfft_radix2_init_f32</a> (<aclass="el"href="structarm__cfft__radix2__instance__f32.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix2_instance_f32</a> *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000005"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000007"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga5c5b2127b3c4ea2d03692127f8543858">arm_cfft_radix2_init_q15</a> (<aclass="el"href="structarm__cfft__radix2__instance__q15.html"title="Instance structure for the Q15 CFFT/CIFFT function.">arm_cfft_radix2_instance_q15</a> *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000006"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed </dd>
<dd><aclass="anchor"id="_deprecated000008"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#gabec9611e77382f31e152668bf6b4b638">arm_cfft_radix2_init_q31</a> (<aclass="el"href="structarm__cfft__radix2__instance__q31.html"title="Instance structure for the Radix-2 Q31 CFFT/CIFFT function.">arm_cfft_radix2_instance_q31</a> *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000007"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000009"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga55b424341dc3efd3fa0bcaaff4bdbf40">arm_cfft_radix2_q15</a> (const <aclass="el"href="structarm__cfft__radix2__instance__q15.html"title="Instance structure for the Q15 CFFT/CIFFT function.">arm_cfft_radix2_instance_q15</a> *S, q15_t *pSrc)</dt>
<dd><aclass="anchor"id="_deprecated000008"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000010"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga6321f703ec87a274aedaab33d3e766b4">arm_cfft_radix2_q31</a> (const <aclass="el"href="structarm__cfft__radix2__instance__q31.html"title="Instance structure for the Radix-2 Q31 CFFT/CIFFT function.">arm_cfft_radix2_instance_q31</a> *S, q31_t *pSrc)</dt>
<dd><aclass="anchor"id="_deprecated000009"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000011"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#gaf1a69e7dd78facf7c430c4640d700266">arm_cfft_radix4_f16</a> (const <aclass="el"href="structarm__cfft__radix4__instance__f16.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix4_instance_f16</a> *S, float16_t *pSrc)</dt>
<dd><aclass="anchor"id="_deprecated000010"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000012"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga521f670cd9c571bc61aff9bec89f4c26">arm_cfft_radix4_f32</a> (const <aclass="el"href="structarm__cfft__radix4__instance__f32.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix4_instance_f32</a> *S, float32_t *pSrc)</dt>
<dd><aclass="anchor"id="_deprecated000011"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000013"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga49454217afb4c46a572d1ec3c8288212">arm_cfft_radix4_init_f16</a> (<aclass="el"href="structarm__cfft__radix4__instance__f16.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix4_instance_f16</a> *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000012"></a>Do not use this function. It has been superceded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000014"></a>Do not use this function. It has been superceded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#gaf336459f684f0b17bfae539ef1b1b78a">arm_cfft_radix4_init_f32</a> (<aclass="el"href="structarm__cfft__radix4__instance__f32.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix4_instance_f32</a> *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000013"></a>Do not use this function. It has been superceded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000015"></a>Do not use this function. It has been superceded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga0c2acfda3126c452e75b81669e8ad9ef">arm_cfft_radix4_init_q15</a> (<aclass="el"href="structarm__cfft__radix4__instance__q15.html"title="Instance structure for the Q15 CFFT/CIFFT function.">arm_cfft_radix4_instance_q15</a> *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000014"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000016"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#gad5caaafeec900c8ff72321c01bbd462c">arm_cfft_radix4_init_q31</a> (<aclass="el"href="structarm__cfft__radix4__instance__q31.html"title="Instance structure for the Q31 CFFT/CIFFT function.">arm_cfft_radix4_instance_q31</a> *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000015"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000017"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#ga8d66cdac41b8bf6cefdb895456eee84a">arm_cfft_radix4_q15</a> (const <aclass="el"href="structarm__cfft__radix4__instance__q15.html"title="Instance structure for the Q15 CFFT/CIFFT function.">arm_cfft_radix4_instance_q15</a> *S, q15_t *pSrc)</dt>
<dd><aclass="anchor"id="_deprecated000016"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000018"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__ComplexFFT.html#gafde3ee1f58cf393b45a9073174fff548">arm_cfft_radix4_q31</a> (const <aclass="el"href="structarm__cfft__radix4__instance__q31.html"title="Instance structure for the Q31 CFFT/CIFFT function.">arm_cfft_radix4_instance_q31</a> *S, q31_t *pSrc)</dt>
<dd><aclass="anchor"id="_deprecated000017"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000019"></a>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__RealFFT.html#ga3df1766d230532bc068fc4ed69d0fcdc">arm_rfft_f32</a> (const <aclass="el"href="structarm__rfft__instance__f32.html"title="Instance structure for the floating-point RFFT/RIFFT function.">arm_rfft_instance_f32</a> *S, float32_t *pSrc, float32_t *pDst)</dt>
<dd><aclass="anchor"id="_deprecated000018"></a>Do not use this function. It has been superceded by <aclass="el"href="group__RealFFT.html#ga5d2ec62f3e35575eba467d09ddcd98b5">arm_rfft_fast_f32</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000020"></a>Do not use this function. It has been superceded by <aclass="el"href="group__RealFFT.html#ga5d2ec62f3e35575eba467d09ddcd98b5">arm_rfft_fast_f32</a> and will be removed in the future. </dd>
<dt>Global <aclass="el"href="group__RealFFT.html#ga10717ee326bf50832ef1c25b85a23068">arm_rfft_init_f32</a> (<aclass="el"href="structarm__rfft__instance__f32.html"title="Instance structure for the floating-point RFFT/RIFFT function.">arm_rfft_instance_f32</a> *S, <aclass="el"href="structarm__cfft__radix4__instance__f32.html"title="Instance structure for the floating-point CFFT/CIFFT function.">arm_cfft_radix4_instance_f32</a> *S_CFFT, uint32_t fftLenReal, uint32_t ifftFlagR, uint32_t bitReverseFlag)</dt>
<dd><aclass="anchor"id="_deprecated000019"></a>Do not use this function. It has been superceded by <aclass="el"href="group__RealFFT.html#gac5fceb172551e7c11eb4d0e17ef15aa3">arm_rfft_fast_init_f32</a> and will be removed in the future. </dd>
<dd><aclass="anchor"id="_deprecated000021"></a>Do not use this function. It has been superceded by <aclass="el"href="group__RealFFT.html#gac5fceb172551e7c11eb4d0e17ef15aa3">arm_rfft_fast_init_f32</a> and will be removed in the future. </dd>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000002">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000004">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point Radix-2 CFFT/CIFFT structure </td></tr>
@ -855,7 +855,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000003">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000005">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point Radix-2 CFFT/CIFFT structure </td></tr>
@ -904,7 +904,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000004">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000006">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point CFFT/CIFFT structure </td></tr>
@ -971,7 +971,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000005">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000007">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point CFFT/CIFFT structure </td></tr>
@ -1038,7 +1038,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000006">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000008">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the Q15 CFFT/CIFFT structure. </td></tr>
@ -1105,7 +1105,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000007">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000009">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the Q31 CFFT/CIFFT structure </td></tr>
@ -1160,7 +1160,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000008">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000010">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the fixed-point CFFT/CIFFT structure </td></tr>
@ -1197,7 +1197,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000009">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000011">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the fixed-point CFFT/CIFFT structure </td></tr>
@ -1234,7 +1234,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000010">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000012">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point Radix-4 CFFT/CIFFT structure </td></tr>
@ -1271,7 +1271,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000011">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000013">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point Radix-4 CFFT/CIFFT structure </td></tr>
@ -1320,7 +1320,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000012">Deprecated:</a></b></dt><dd>Do not use this function. It has been superceded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000014">Deprecated:</a></b></dt><dd>Do not use this function. It has been superceded by <aclass="el"href="group__ComplexFFT.html#ga4a780db4d709212ee89f7646a7875fdb">arm_cfft_f16</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point CFFT/CIFFT structure </td></tr>
@ -1387,7 +1387,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000013">Deprecated:</a></b></dt><dd>Do not use this function. It has been superceded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000015">Deprecated:</a></b></dt><dd>Do not use this function. It has been superceded by <aclass="el"href="group__ComplexFFT.html#gade0f9c4ff157b6b9c72a1eafd86ebf80">arm_cfft_f32</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point CFFT/CIFFT structure </td></tr>
@ -1454,7 +1454,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000014">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000016">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the Q15 CFFT/CIFFT structure </td></tr>
@ -1521,7 +1521,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000015">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000017">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the Q31 CFFT/CIFFT structure. </td></tr>
@ -1576,7 +1576,7 @@ Functions</h2></td></tr>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000016">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000018">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga68cdacd2267a2967955e40e6b7ec1229">arm_cfft_q15</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the Q15 CFFT/CIFFT structure. </td></tr>
<dlclass="section user"><dt>Input and output formats:</dt><dd>Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process. Hence the output format is different for different FFT sizes. The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT: </dd></dl>
Input and Output Formats for Q15 CIFFT</div></div>
</dd></dl>
<dlclass="section user"><dt></dt><dd></dd></dl>
<tableclass="markdownTable">
<trclass="markdownTableHead">
<thclass="markdownTableHeadRight">CFFT Size </th><thclass="markdownTableHeadRight">Input format </th><thclass="markdownTableHeadRight">Output format </th><thclass="markdownTableHeadRight">Number of bits to upscale </th></tr>
<thclass="markdownTableHeadRight">CIFFT Size </th><thclass="markdownTableHeadRight">Input format </th><thclass="markdownTableHeadRight">Output format </th><thclass="markdownTableHeadRight">Number of bits to upscale </th></tr>
@ -1623,7 +1639,7 @@ Input and Output Formats for Q15 CIFFT</div></div>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000017">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000019">Deprecated:</a></b></dt><dd>Do not use this function. It has been superseded by <aclass="el"href="group__ComplexFFT.html#ga5a0008bd997ab6e2e299ef2fb272fb4b">arm_cfft_q31</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the Q31 CFFT/CIFFT structure </td></tr>
@ -1633,15 +1649,31 @@ Input and Output Formats for Q15 CIFFT</div></div>
<dlclass="section user"><dt>Input and output formats:</dt><dd>Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process. Hence the output format is different for different FFT sizes. The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT: </dd></dl>
Input and Output Formats for Q31 CIFFT</div></div>
</dd></dl>
<dlclass="section user"><dt></dt><dd></dd></dl>
<tableclass="markdownTable">
<trclass="markdownTableHead">
<thclass="markdownTableHeadRight">CFFT Size </th><thclass="markdownTableHeadRight">Input format </th><thclass="markdownTableHeadRight">Output format </th><thclass="markdownTableHeadRight">Number of bits to upscale </th></tr>
<thclass="markdownTableHeadRight">CIFFT Size </th><thclass="markdownTableHeadRight">Input format </th><thclass="markdownTableHeadRight">Output format </th><thclass="markdownTableHeadRight">Number of bits to upscale </th></tr>
<p>Convolution is a mathematical operation that operates on two finite length vectors to generate a finite length output vector. Convolution is similar to correlation and is frequently used in filtering and data analysis. The CMSIS DSP library contains functions for convolving Q7, Q15, Q31, and floating-point data types. The library also provides fast versions of the Q15 and Q31 functions.</p>
<dlclass="section user"><dt>Algorithm</dt><dd>Let <code>a[n]</code> and <code>b[n]</code> be sequences of length <code>srcALen</code> and <code>srcBLen</code> samples respectively. Then the convolution <pre>
c[n] = a[n] * b[n]
</pre></dd></dl>
<dlclass="section user"><dt></dt><dd>is defined as <divclass="image">
<imgsrc="ConvolutionEquation.gif"alt=""/>
</div>
<dlclass="section user"><dt>Algorithm</dt><dd>Let <code>a[n]</code> and <code>b[n]</code> be sequences of length <code>srcALen</code> and <code>srcBLen</code> samples respectively. Then the convolution <pclass="formulaDsp">
\[ c[n] = a[n] * b[n] \]
</p>
</dd></dl>
<dlclass="section user"><dt></dt><dd>is defined as <pclass="formulaDsp">
\[ c[n] = \sum_{k=0}^{srcALen} a[k] b[n-k] \]
</p>
</dd></dl>
<dlclass="section user"><dt></dt><dd>Note that <code>c[n]</code> is of length <code>srcALen + srcBLen - 1</code> and is defined over the interval <code>n=0, 1, 2, ..., srcALen + srcBLen - 2</code>. <code>pSrcA</code> points to the first input vector of length <code>srcALen</code> and <code>pSrcB</code> points to the second input vector of length <code>srcBLen</code>. The output result is written to <code>pDst</code> and the calling function must allocate <code>srcALen+srcBLen-1</code> words for the result. </dd></dl>
<dlclass="section user"><dt></dt><dd>Conceptually, when two signals <code>a[n]</code> and <code>b[n]</code> are convolved, the signal <code>b[n]</code> slides over <code>a[n]</code>. For each offset <code>n</code>, the overlapping portions of a[n] and b[n] are multiplied and summed together. </dd></dl>
<dlclass="section user"><dt></dt><dd>Note that convolution is a commutative operation: <pre>
a[n] * b[n] = b[n] * a[n].
</pre></dd></dl>
<dlclass="section user"><dt></dt><dd>Note that convolution is a commutative operation: <pclass="formulaDsp">
\[ a[n] * b[n] = b[n] * a[n]. \]
</p>
</dd></dl>
<dlclass="section user"><dt></dt><dd>This means that switching the A and B arguments to the convolution functions has no effect.</dd></dl>
<dlclass="section user"><dt>Fixed-Point Behavior</dt><dd>Convolution requires summing up a large number of intermediate products. As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation. Refer to the function specific documentation below for further details of the particular algorithm used.</dd></dl>
<dlclass="section user"><dt>Fast Versions</dt><dd>Fast versions are supported for Q31 and Q15. Cycles for Fast versions are less compared to Q31 and Q15 of conv and the design requires the input signals should be scaled down to avoid intermediate overflows.</dd></dl>
<p>Correlation is a mathematical operation that is similar to convolution. As with convolution, correlation uses two signals to produce a third signal. The underlying algorithms in correlation and convolution are identical except that one of the inputs is flipped in convolution. Correlation is commonly used to measure the similarity between two signals. It has applications in pattern recognition, cryptanalysis, and searching. The CMSIS library provides correlation functions for Q7, Q15, Q31 and floating-point data types. Fast versions of the Q15 and Q31 functions are also provided.</p>
<dlclass="section user"><dt>Algorithm</dt><dd>Let <code>a[n]</code> and <code>b[n]</code> be sequences of length <code>srcALen</code> and <code>srcBLen</code> samples respectively. The convolution of the two signals is denoted by <pre>
c[n] = a[n] * b[n]
</pre> In correlation, one of the signals is flipped in time <pre>
c[n] = a[n] * b[-n]
</pre></dd></dl>
<dlclass="section user"><dt></dt><dd>and this is mathematically defined as <divclass="image">
<imgsrc="CorrelateEquation.gif"alt=""/>
</div>
<dlclass="section user"><dt>Algorithm</dt><dd>Let <code>a[n]</code> and <code>b[n]</code> be sequences of length <code>srcALen</code> and <code>srcBLen</code> samples respectively. The convolution of the two signals is denoted by <pclass="formulaDsp">
\[ c[n] = a[n] * b[n] \]
</p>
</dd></dl>
<p>In correlation, one of the signals is flipped in time</p>
<pclass="formulaDsp">
\[ c[n] = a[n] * b[-n] \]
</p>
<dlclass="section user"><dt></dt><dd>and this is mathematically defined as <pclass="formulaDsp">
\[ c[n] = \sum_{k=0}^{srcALen} a[k] b[k-n] \]
</p>
</dd></dl>
<dlclass="section user"><dt></dt><dd>The <code>pSrcA</code> points to the first input vector of length <code>srcALen</code> and <code>pSrcB</code> points to the second input vector of length <code>srcBLen</code>. The result <code>c[n]</code> is of length <code>2 * max(srcALen, srcBLen) - 1</code> and is defined over the interval <code>n=0, 1, 2, ..., (2 * max(srcALen, srcBLen) - 2)</code>. The output result is written to <code>pDst</code> and the calling function must allocate <code>2 * max(srcALen, srcBLen) - 1</code> words for the result.</dd></dl>
<dlclass="section note"><dt>Note</dt><dd>The <code>pDst</code> should be initialized to all zeros before being used.</dd></dl>
<dlclass="section user"><dt>Algorithm</dt><dd>The N-point type-IV DCT is defined as a real, linear transformation by the formula: <div class="image">
<imgsrc="DCT4Equation.gif"alt=""/>
</div>
<dlclass="section user"><dt>Algorithm</dt><dd>The N-point type-IV DCT is defined as a real, linear transformation by the formula: <p class="formulaDsp">
where <code>n = 0, 1, 2, ..., N-1</code></dd></dl>
<dlclass="section user"><dt></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>
<dlclass="section user"><dt>Lengths supported by the transform:</dt><dd>As DCT4 internally uses Real FFT, it supports all the lengths 128, 512, 2048 and 8192. The library provides separate functions for Q15, Q31, and floating-point data types.</dd></dl>
<dlclass="section user"><dt>Normalizing factor</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:</dd></dl>
<divclass="image">
<imgsrc="dct4NormalizingF32Table.gif"alt=""/>
</div>
<tableclass="markdownTable">
<trclass="markdownTableHead">
<thclass="markdownTableHeadRight">DCT Size </th><thclass="markdownTableHeadRight">Normalizing factor value </th></tr>
<dlclass="section user"><dt>Normalizing factor</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:</dd></dl>
<divclass="image">
<imgsrc="dct4NormalizingQ15Table.gif"alt=""/>
</div>
<tableclass="markdownTable">
<trclass="markdownTableHead">
<thclass="markdownTableHeadRight">DCT Size </th><thclass="markdownTableHeadRight">Normalizing factor value (hexadecimal) </th></tr>
<dlclass="section user"><dt>Normalizing factor:</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:</dd></dl>
<divclass="image">
<imgsrc="dct4NormalizingQ31Table.gif"alt=""/>
</div>
<tableclass="markdownTable">
<trclass="markdownTableHead">
<thclass="markdownTableHeadRight">DCT Size </th><thclass="markdownTableHeadRight">Normalizing factor value (hexadecimal) </th></tr>
<dlclass="section user"><dt>Input an output formats</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>
<divclass="image">
<imgsrc="dct4FormatsQ15Table.gif"alt=""/>
</div>
<tableclass="markdownTable">
<trclass="markdownTableHead">
<thclass="markdownTableHeadRight">DCT Size </th><thclass="markdownTableHeadRight">Input format </th><thclass="markdownTableHeadRight">Output format </th><thclass="markdownTableHeadRight">Number of bits to upscale </th></tr>
<dlclass="section user"><dt>Input an output formats</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>
<divclass="image">
<imgsrc="dct4FormatsQ31Table.gif"alt=""/>
</div>
<tableclass="markdownTable">
<trclass="markdownTableHead">
<thclass="markdownTableHeadRight">DCT Size </th><thclass="markdownTableHeadRight">Input format </th><thclass="markdownTableHeadRight">Output format </th><thclass="markdownTableHeadRight">Number of bits to upscale </th></tr>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000002">Deprecated:</a></b></dt><dd>Those functions are no more tested nor maintained and will be removed in a future version.</dd></dl>
<p>This set of functions implements Finite Impulse Response (FIR) lattice filters for Q15, Q31 and floating-point data types. Lattice filters are used in a variety of adaptive filter applications. The filter structure is feedforward and the net impulse response is finite length. The functions operate on blocks of input and output data and each call to the function processes <code>blockSize</code> samples through the filter. <code>pSrc</code> and <code>pDst</code> point to input and output arrays containing <code>blockSize</code> values.</p>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000003">Deprecated:</a></b></dt><dd>Those functions are no more tested nor maintained and will be removed in a future version.</dd></dl>
<p>This group of functions implements sparse FIR filters. Sparse FIR filters are equivalent to standard FIR filters except that most of the coefficients are equal to zero. Sparse filters are used for simulating reflections in communications and audio applications.</p>
<p>There are separate functions for Q7, Q15, Q31, and floating-point data types. The functions operate on blocks of input and output data and each call to the function processes <code>blockSize</code> samples through the filter. <code>pSrc</code> and <code>pDst</code> points to input and output arrays respectively containing <code>blockSize</code> values.</p>
<dlclass="section user"><dt>Algorithm</dt><dd>The sparse filter instant structure contains an array of tap indices <code>pTapDelay</code> which specifies the locations of the non-zero coefficients. This is in addition to the coefficient array <code>b</code>. The implementation essentially skips the multiplications by zero and leads to an efficient realization. <pre>
<p>Adds two matrices. </p><dl class="section user"><dt>Addition of two 3 x 3 matrices</dt><dd></dd></dl>
<p class="formulaDsp">
\[ \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \\ a_{2,1} & a_{2,2} & a_{2,3} \\ a_{3,1} & a_{3,2} & a_{3,3} \\ \end{pmatrix} + \begin{pmatrix} b_{1,1} & b_{1,2} & b_{1,3} \\ b_{2,1} & b_{2,2} & b_{2,3} \\ b_{3,1} & b_{3,2} & b_{3,3} \\ \end{pmatrix} = \begin{pmatrix} a_{1,1}+b_{1,1} & a_{1,2}+b_{1,2} & a_{1,3}+b_{1,3} \\ a_{2,1}+b_{2,1} & a_{2,2}+b_{2,2} & a_{2,3}+b_{2,3} \\ a_{3,1}+b_{3,1} & a_{3,2}+b_{3,2} & a_{3,3}+b_{3,3} \\ \end{pmatrix} \]
</p>
<p>The functions check to make sure that <code>pSrcA</code>, <code>pSrcB</code>, and <code>pDst</code> have the same number of rows and columns. </p>
<p>Transposing an <code>M x N</code> matrix flips it around the center diagonal and results in an <code>N x M</code> matrix. </p><divclass="image">
<imgsrc="MatrixTranspose.gif"alt=""/>
<divclass="caption">
Transpose of a 3 x 3 matrix</div></div>
<p>Transposing an <code>M x N</code> matrix flips it around the center diagonal and results in an <code>N x M</code> matrix.</p>
<dlclass="section user"><dt>Transpose of a 3 x 3 matrix</dt><dd></dd></dl>
<pclass="formulaDsp">
\[ \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \\ a_{2,1} & a_{2,2} & a_{2,3} \\ a_{3,1} & a_{3,2} & a_{3,3} \\ \end{pmatrix}^T = \begin{pmatrix} a_{1,1} & a_{2,1} & a_{3,1} \\ a_{1,2} & a_{2,2} & a_{3,2} \\ a_{1,3} & a_{2,3} & a_{3,3} \\ \end{pmatrix} \]
<p>The inverse is defined only if the input matrix is square and non-singular (the determinant is non-zero). The function checks that the input and output matrices are square and of the same size.</p>
<p>Matrix inversion is numerically sensitive and the CMSIS DSP library only supports matrix inversion of floating-point matrices.</p>
<dlclass="section user"><dt>Algorithm</dt><dd>The Gauss-Jordan method is used to find the inverse. The algorithm performs a sequence of elementary row-operations until it reduces the input matrix to an identity matrix. Applying the same sequence of elementary row-operations to an identity matrix yields the inverse matrix. If the input matrix is singular, then the algorithm terminates and returns error status <code>ARM_MATH_SINGULAR</code>.<divclass="image">
<img src="MatrixInverse.gif"alt=""/>
<div class="caption">
Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method</div></div>
<dlclass="section user"><dt>Algorithm</dt><dd>The Gauss-Jordan method is used to find the inverse. The algorithm performs a sequence of elementary row-operations until it reduces the input matrix to an identity matrix. Applying the same sequence of elementary row-operations to an identity matrix yields the inverse matrix. If the input matrix is singular, then the algorithm terminates and returns error status <code>ARM_MATH_SINGULAR</code>.</dd></dl>
<dl class="section user"><dt>Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method </dt><dd></dd></dl>
<p class="formulaDsp">
\[ \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} & | & 1 & 0 & 0\\ a_{2,1} & a_{2,2} & a_{2,3} & | & 0 & 1 & 0\\ a_{3,1} & a_{3,2} & a_{3,3} & | & 0 & 0 & 1\\ \end{pmatrix} \rightarrow \begin{pmatrix} 1 & 0 & 0 & | & x_{1,1} & x_{2,1} & x_{3,1} \\ 0 & 1 & 0 & | & x_{1,2} & x_{2,2} & x_{3,2} \\ 0 & 0 & 1 & | & x_{1,3} & x_{2,3} & x_{3,3} \\ \end{pmatrix} \]
<p>Multiplies a matrix by a scalar. This is accomplished by multiplying each element in the matrix by the scalar. For example: </p><divclass="image">
<imgsrc="MatrixScale.gif"alt=""/>
<divclass="caption">
Matrix Scaling of a 3 x 3 matrix</div></div>
<p>Multiplies a matrix by a scalar. This is accomplished by multiplying each element in the matrix by the scalar. For example:</p>
<dlclass="section user"><dt>Matrix Scaling of a 3 x 3 matrix </dt><dd></dd></dl>
<pclass="formulaDsp">
\[ \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \\ a_{2,1} & a_{2,2} & a_{2,3} \\ a_{3,1} & a_{3,2} & a_{3,3} \\ \end{pmatrix} K = \begin{pmatrix} K a_{1,1} & K a_{1,2} & K a_{1,3} \\ K a_{2,1} & K a_{2,2} & K a_{2,3} \\ K a_{3,1} & K a_{3,2} & K a_{3,3} \\ \end{pmatrix} \]
</p>
<p>The function checks to make sure that the input and output matrices are of the same size.</p>
<p>In the fixed-point Q15 and Q31 functions, <code>scale</code> is represented by a fractional multiplication <code>scaleFract</code> and an arithmetic shift <code>shift</code>. The shift allows the gain of the scaling operation to exceed 1.0. The overall scale factor applied to the fixed-point data is </p><pre>
<p>The functions check to make sure that <code>pSrcA</code>, <code>pSrcB</code>, and <code>pDst</code> have the same number of rows and columns. </p>
<p>Subtract two matrices. </p><dl class="section user"><dt>Subraction of two 3 x 3 matrices</dt><dd></dd></dl>
<p class="formulaDsp">
\[ \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \\ a_{2,1} & a_{2,2} & a_{2,3} \\ a_{3,1} & a_{3,2} & a_{3,3} \\ \end{pmatrix} - \begin{pmatrix} b_{1,1} & b_{1,2} & b_{1,3} \\ b_{2,1} & b_{2,2} & b_{2,3} \\ b_{3,1} & b_{3,2} & b_{3,3} \\ \end{pmatrix} = \begin{pmatrix} a_{1,1}-b_{1,1} & a_{1,2}-b_{1,2} & a_{1,3}-b_{1,3} \\ a_{2,1}-b_{2,1} & a_{2,2}-b_{2,2} & a_{2,3}-b_{2,3} \\ a_{3,1}-b_{3,1} & a_{3,2}-b_{3,2} & a_{3,3}-b_{3,3} \\ \end{pmatrix} \]
</p>
<p>The functions check to make sure that <code>pSrcA</code>, <code>pSrcB</code>, and <code>pDst</code> have the same number of rows and columns. </p>
<p>Transposing an <code>M x N</code> matrix flips it around the center diagonal and results in an <code>N x M</code> matrix. </p><divclass="image">
<imgsrc="MatrixTranspose.gif"alt=""/>
<divclass="caption">
Transpose of a 3 x 3 matrix</div></div>
<p>Transposing an <code>M x N</code> matrix flips it around the center diagonal and results in an <code>N x M</code> matrix.</p>
<dlclass="section user"><dt>Transpose of a 3 x 3 matrix</dt><dd></dd></dl>
<pclass="formulaDsp">
\[ \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \\ a_{2,1} & a_{2,2} & a_{2,3} \\ a_{3,1} & a_{3,2} & a_{3,3} \\ \end{pmatrix}^T = \begin{pmatrix} a_{1,1} & a_{2,1} & a_{3,1} \\ a_{1,2} & a_{2,2} & a_{3,2} \\ a_{1,3} & a_{2,3} & a_{3,3} \\ \end{pmatrix} \]
@ -240,7 +240,7 @@ Real Inverse Fast Fourier Transform</div></div>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000018">Deprecated:</a></b></dt><dd>Do not use this function. It has been superceded by <aclass="el"href="group__RealFFT.html#ga5d2ec62f3e35575eba467d09ddcd98b5">arm_rfft_fast_f32</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000020">Deprecated:</a></b></dt><dd>Do not use this function. It has been superceded by <aclass="el"href="group__RealFFT.html#ga5d2ec62f3e35575eba467d09ddcd98b5">arm_rfft_fast_f32</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point RFFT/RIFFT structure </td></tr>
@ -585,7 +585,7 @@ Real Inverse Fast Fourier Transform</div></div>
</tr>
</table>
</div><divclass="memdoc">
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000019">Deprecated:</a></b></dt><dd>Do not use this function. It has been superceded by <aclass="el"href="group__RealFFT.html#gac5fceb172551e7c11eb4d0e17ef15aa3">arm_rfft_fast_init_f32</a> and will be removed in the future. </dd></dl>
<dlclass="deprecated"><dt><b><aclass="el"href="deprecated.html#_deprecated000021">Deprecated:</a></b></dt><dd>Do not use this function. It has been superceded by <aclass="el"href="group__RealFFT.html#gac5fceb172551e7c11eb4d0e17ef15aa3">arm_rfft_fast_init_f32</a> and will be removed in the future. </dd></dl>
<dlclass="params"><dt>Parameters</dt><dd>
<tableclass="params">
<tr><tdclass="paramdir">[in,out]</td><tdclass="paramname">S</td><td>points to an instance of the floating-point RFFT/RIFFT structure </td></tr>
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