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DSP_fft32x32s

4-28

Complex Forward Mixed Radix 32 x 32-bit FFT With Scaling

DSP_fft32x32s

Function void DSP_fft32x32s(const int * restrict w, int nx, int * restrict x, int * restrict y)

Arguments w[2*nx] Pointer to complex 32-bit FFT coefficients.

nx Length of FFT in complex samples. Must be power of 2 or 4,

and 16 ≤ nx ≤ 32768.

x[2*nx] Pointer to complex 32-bit data input.

y[2*nx] Pointer to complex 32-bit data output.

Description This routine computes an extended precision complex forward mixed radix

FFT with scaling, rounding and digit reversal. Input data x[ ], output data y[ ],

and coefficients w[ ] are 32-bit. The output is returned in the separate array y[ ]

in normal order. Each complex value is stored with interleaved real and

imaginary parts. The code uses a special ordering of FFT coefficients (also

called twiddle factors) and memory accesses to improve performance in the

presence of cache. The C code to generate the twiddle factors is the same one

used for the DSP_fft32x32 routine.

Scaling by 2 (i.e., >>1) takes place at each radix-4 stage except for the last

one. A radix-4 stage can add a maximum of 2 bits, which would require scaling

by 4 to completely prevent overflow. Thus, the input data must be scaled by

log2(nx)−ceil[log4(nx)−1])

Algorithm The C equivalent of the assembly code without restrictions is similar to the one

shown for the fft16x16t routine. For further details, see the source code of the

C version of this function, which is provided with this library. Note that the

assembly code is hand optimized and restrictions may apply.

Special Requirements

- In-place computation is not allowed.

- The size of the FFT, nx, must be a power of 4 or 2 and greater than or equal

to 16 and less than 32768.

- The arrays for the complex input data x[ ], complex output data y[ ], and

twiddle factors w[ ] must be double-word aligned.

- The input and output data are complex, with the real/imaginary

components stored in adjacent locations in the array. The real

components are stored at even array indices, and the imaginary

components are stored at odd array indices.

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