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@ -604,162 +604,6 @@ extern void arm_radix4_butterfly_f16(
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@ingroup groupTransforms
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*/
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/**
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@defgroup ComplexFFT Complex FFT Functions
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@par
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The Fast Fourier Transform (FFT) is an efficient algorithm for computing the
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Discrete Fourier Transform (DFT). The FFT can be orders of magnitude faster
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than the DFT, especially for long lengths.
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The algorithms described in this section
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operate on complex data. A separate set of functions is devoted to handling
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of real sequences.
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@par
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There are separate algorithms for handling floating-point, Q15, and Q31 data
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types. The algorithms available for each data type are described next.
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@par
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The FFT functions operate in-place. That is, the array holding the input data
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will also be used to hold the corresponding result. The input data is complex
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and contains <code>2*fftLen</code> interleaved values as shown below.
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<pre>{real[0], imag[0], real[1], imag[1], ...} </pre>
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The FFT result will be contained in the same array and the frequency domain
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values will have the same interleaving.
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@par Floating-point
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The floating-point complex FFT uses a mixed-radix algorithm. Multiple radix-8
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stages are performed along with a single radix-2 or radix-4 stage, as needed.
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The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses
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a different twiddle factor table.
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@par
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The function uses the standard FFT definition and output values may grow by a
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factor of <code>fftLen</code> when computing the forward transform. The
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inverse transform includes a scale of <code>1/fftLen</code> as part of the
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calculation and this matches the textbook definition of the inverse FFT.
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@par
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For the MVE version, the new arm_cfft_init_f32 initialization function is
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<b>mandatory</b>. <b>Compilation flags are available to include only the required tables for the
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needed FFTs.</b> Other FFT versions can continue to be initialized as
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explained below.
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@par
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For not MVE versions, pre-initialized data structures containing twiddle factors
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and bit reversal tables are provided and defined in <code>arm_const_structs.h</code>. Include
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this header in your function and then pass one of the constant structures as
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an argument to arm_cfft_f32. For example:
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@par
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<code>arm_cfft_f32(arm_cfft_sR_f32_len64, pSrc, 1, 1)</code>
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@par
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computes a 64-point inverse complex FFT including bit reversal.
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The data structures are treated as constant data and not modified during the
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calculation. The same data structure can be reused for multiple transforms
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including mixing forward and inverse transforms.
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@par
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Earlier releases of the library provided separate radix-2 and radix-4
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algorithms that operated on floating-point data. These functions are still
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provided but are deprecated. The older functions are slower and less general
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than the new functions.
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@par
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An example of initialization of the constants for the arm_cfft_f32 function follows:
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@code
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const static arm_cfft_instance_f32 *S;
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...
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switch (length) {
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case 16:
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S = &arm_cfft_sR_f32_len16;
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break;
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case 32:
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S = &arm_cfft_sR_f32_len32;
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break;
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case 64:
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S = &arm_cfft_sR_f32_len64;
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break;
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case 128:
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S = &arm_cfft_sR_f32_len128;
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break;
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case 256:
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S = &arm_cfft_sR_f32_len256;
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break;
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case 512:
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S = &arm_cfft_sR_f32_len512;
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break;
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case 1024:
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S = &arm_cfft_sR_f32_len1024;
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break;
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case 2048:
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S = &arm_cfft_sR_f32_len2048;
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break;
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case 4096:
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S = &arm_cfft_sR_f32_len4096;
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break;
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}
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@endcode
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@par
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The new arm_cfft_init_f32 can also be used.
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@par Q15 and Q31
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The floating-point complex FFT uses a mixed-radix algorithm. Multiple radix-4
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stages are performed along with a single radix-2 stage, as needed.
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The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses
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a different twiddle factor table.
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@par
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The function uses the standard FFT definition and output values may grow by a
|
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|
|
|
factor of <code>fftLen</code> when computing the forward transform. The
|
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|
|
|
inverse transform includes a scale of <code>1/fftLen</code> as part of the
|
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|
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|
calculation and this matches the textbook definition of the inverse FFT.
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@par
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Pre-initialized data structures containing twiddle factors and bit reversal
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tables are provided and defined in <code>arm_const_structs.h</code>. Include
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this header in your function and then pass one of the constant structures as
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an argument to arm_cfft_q31. For example:
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@par
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<code>arm_cfft_q31(arm_cfft_sR_q31_len64, pSrc, 1, 1)</code>
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@par
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computes a 64-point inverse complex FFT including bit reversal.
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The data structures are treated as constant data and not modified during the
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calculation. The same data structure can be reused for multiple transforms
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including mixing forward and inverse transforms.
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@par
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Earlier releases of the library provided separate radix-2 and radix-4
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|
|
|
algorithms that operated on floating-point data. These functions are still
|
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|
|
|
provided but are deprecated. The older functions are slower and less general
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|
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than the new functions.
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@par
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An example of initialization of the constants for the arm_cfft_q31 function follows:
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@code
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const static arm_cfft_instance_q31 *S;
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...
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switch (length) {
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case 16:
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S = &arm_cfft_sR_q31_len16;
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break;
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case 32:
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S = &arm_cfft_sR_q31_len32;
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break;
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case 64:
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S = &arm_cfft_sR_q31_len64;
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break;
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case 128:
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S = &arm_cfft_sR_q31_len128;
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break;
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case 256:
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S = &arm_cfft_sR_q31_len256;
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break;
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case 512:
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S = &arm_cfft_sR_q31_len512;
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break;
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case 1024:
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S = &arm_cfft_sR_q31_len1024;
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break;
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case 2048:
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S = &arm_cfft_sR_q31_len2048;
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break;
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case 4096:
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S = &arm_cfft_sR_q31_len4096;
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break;
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}
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@endcode
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*/
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/**
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@addtogroup ComplexFFT
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@{
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Christophe Favergeon
3 years ago