dsp_fft16x16t.h64
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H64
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;* ======================================================================== *;
;* TEXAS INSTRUMENTS, INC. *;
;* *;
;* DSPLIB DSP Signal Processing Library *;
;* *;
;* Release: Revision 1.04b *;
;* CVS Revision: 1.7 Sun Sep 29 03:32:21 2002 (UTC) *;
;* Snapshot date: 23-Oct-2003 *;
;* *;
;* This library contains proprietary intellectual property of Texas *;
;* Instruments, Inc. The library and its source code are protected by *;
;* various copyrights, and portions may also be protected by patents or *;
;* other legal protections. *;
;* *;
;* This software is licensed for use with Texas Instruments TMS320 *;
;* family DSPs. This license was provided to you prior to installing *;
;* the software. You may review this license by consulting the file *;
;* TI_license.PDF which accompanies the files in this library. *;
;* ------------------------------------------------------------------------ *;
;* Copyright (C) 2003 Texas Instruments, Incorporated. *;
;* All Rights Reserved. *;
;* ======================================================================== *;
;* ======================================================================== *;
;* Assembler compatibility shim for assembling 4.30 and later code on *;
;* tools prior to 4.30. *;
;* ======================================================================== *;
;* ======================================================================== *;
;* End of assembler compatibility shim. *;
;* ======================================================================== *;
* ========================================================================= *
* TEXAS INSTRUMENTS, INC. *
* *
* NAME *
* fft: Mixed radix FFT for 2^M and 4^M, 16x16 with truncation *
* *
* *
* REVISION DATE *
* 23-May-2002 *
* *
* USAGE *
* This routine is C-callable and can be called as: *
* *
* void DSP_fft16x16t(const short * ptr_w, int npoints, short * ptr_x, *
* short * ptr_y) *
* *
* where: *
* ptr_w: pointer to an array of twiddle factors generated as explained *
* below. *
* npoints: Number of points for the FFT transform, can be a multiple of *
* 2 or 4. *
* ptr_x: Pointer to input data to be transformed. *
* ptr_y: Pointer that contains the final FFT results in normal order. *
* *
* DESCRIPTION *
* This code performs a mixed radix FFT with digit reversal. The code *
* uses a special ordering of twiddle factors and memory accesses *
* to improve performance in the presence of cache. It operates *
* largely in-place, but the final digit-reversed output is written *
* out-of-place. *
* *
* This code requires a special sequence of twiddle factors stored *
* in Q.15 fixed-point format. The following C code illustrates *
* one way to generate the desired twiddle-factor array: *
* *
* #include <math.h> *
* *
* #ifndef PI *
* # define PI (3.14159265358979323846) *
* #endif *
* *
* short d2s(double d) *
* { *
* d = floor(0.5 + d); /* Explicit rounding to integer */ *
* if (d >= 32767.0) return 32767; *
* if (d <= -32768.0) return -32768; *
* return (short)d; *
* } *
* *
* void gen_twiddle(short *w, int n) *
* { *
* double M = 32767.5; *
* int i, j, k; *
* *
* for (j = 1, k = 0; j < n >> 2; j = j << 2) *
* { *
* for (i = 0; i < n >> 2; i += j << 1) *
* { *
* w[k + 11] = d2s(M * cos(6.0 * PI * (i + j) / n)); *
* w[k + 10] = d2s(M * sin(6.0 * PI * (i + j) / n)); *
* w[k + 9] = d2s(M * cos(6.0 * PI * (i ) / n)); *
* w[k + 8] = d2s(M * sin(6.0 * PI * (i ) / n)); *
* *
* w[k + 7] = d2s(M * cos(4.0 * PI * (i + j) / n)); *
* w[k + 6] = d2s(M * sin(4.0 * PI * (i + j) / n)); *
* w[k + 5] = d2s(M * cos(4.0 * PI * (i ) / n)); *
* w[k + 4] = d2s(M * sin(4.0 * PI * (i ) / n)); *
* *
* w[k + 3] = d2s(M * cos(2.0 * PI * (i + j) / n)); *
* w[k + 2] = d2s(M * sin(2.0 * PI * (i + j) / n)); *
* w[k + 1] = d2s(M * cos(2.0 * PI * (i ) / n)); *
* w[k + 0] = d2s(M * sin(2.0 * PI * (i ) / n)); *
* *
* k += 12; *
* } *
* } *
* w[2*n - 1] = w[2*n - 3] = w[2*n - 5] = 32767; *
* w[2*n - 2] = w[2*n - 4] = w[2*n - 6] = 0; *
* } *
* *
* ASSUMPTIONS *
* The size of the FFT, n, must be a power of 4 or 2 and greater than *
* or equal to 16 and less than 32768. *
* *
* The arrays 'x[]', 'y[]', and 'w[]' all must be aligned on a *
* double-word boundary for the "optimized" implementations. *
* *
* 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. *
* *
* TECHNIQUES *
* The following C code represents an implementation of the Cooley *
* Tukey radix 4 DIF FFT. It accepts the inputs in normal order and *
* produces the outputs in digit reversed order. The natural C code *
* shown in this file on the other hand, accepts the inputs in nor- *
* mal order and produces the outputs in normal order. *
* *
* Several transformations have been applied to the original Cooley *
* Tukey code to produce the natural C code description shown here. *
* In order to understand these it would first be educational to *
* understand some of the issues involved in the conventional Cooley *
* Tukey FFT code. *
* *
* void radix4(int n, short x[], short wn[]) *
* { *
* int n1, n2, ie, ia1, ia2, ia3; *
* int i0, i1, i2, i3, i, j, k; *
* short co1, co2, co3, si1, si2, si3; *
* short xt0, yt0, xt1, yt1, xt2, yt2; *
* short xh0, xh1, xh20, xh21, xl0, xl1,xl20,xl21; *
* *
* n2 = n; *
* ie = 1; *
* for (k = n; k > 1; k >>= 2) *
* { *
* n1 = n2; *
* n2 >>= 2; *
* ia1 = 0; *
* *
* for (j = 0; j < n2; j++) *
* { *
* ia2 = ia1 + ia1; *
* ia3 = ia2 + ia1; *
* *
* co1 = wn[2 * ia1 ]; *
* si1 = wn[2 * ia1 + 1]; *
* co2 = wn[2 * ia2 ]; *
* si2 = wn[2 * ia2 + 1]; *
* co3 = wn[2 * ia3 ]; *
* si3 = wn[2 * ia3 + 1]; *
* ia1 = ia1 + ie; *
* *
* for (i0 = j; i0< n; i0 += n1) *
* { *
* i1 = i0 + n2; *
* i2 = i1 + n2; *
* i3 = i2 + n2; *
* *
* *
* xh0 = x[2 * i0 ] + x[2 * i2 ]; *
* xh1 = x[2 * i0 + 1] + x[2 * i2 + 1]; *
* xl0 = x[2 * i0 ] - x[2 * i2 ]; *
* xl1 = x[2 * i0 + 1] - x[2 * i2 + 1]; *
* *
* xh20 = x[2 * i1 ] + x[2 * i3 ]; *
* xh21 = x[2 * i1 + 1] + x[2 * i3 + 1]; *
* xl20 = x[2 * i1 ] - x[2 * i3 ]; *
* xl21 = x[2 * i1 + 1] - x[2 * i3 + 1]; *
* *
* x[2 * i0 ] = xh0 + xh20; *
* x[2 * i0 + 1] = xh1 + xh21; *
* *
* xt0 = xh0 - xh20; *
* yt0 = xh1 - xh21; *
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