Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 10-Nov-2026 14:19:50 slow_fourier_transform_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 slow_fourier_transform() implements a set of "slow" Fourier transforms. c8mat_sft_test(): c8mat_sftf() computes the forward slow Fourier transform. c8mat_sftb() computes the backward slow Fourier transform. The data has dimension N1 = 10 by N2 = 4 The data X: Col: 1 2 3 4 Row --- 1: 0.537667 -0.102242 -1.349887 -0.863653 0.671497 -1.089064 0.888396 -0.615602 2: 1.833885 -0.241447 3.034923 0.077359 -1.207487 0.032557 -1.147070 0.748077 3: -2.258847 0.319207 0.725404 -1.214117 0.717239 0.552527 -1.068870 -0.192419 4: 0.862173 0.312859 -0.063055 -1.113501 1.630235 1.100610 -0.809499 0.888610 5: 0.318765 -0.864880 0.714743 -0.006849 0.488894 1.544212 -2.944284 -0.764849 6: -1.307688 -0.030051 -0.204966 1.532630 1.034693 0.085931 1.438380 -1.402269 7: -0.433592 -0.164879 -0.124144 -0.769666 0.726885 -1.491590 0.325191 -1.422376 8: 0.342624 0.627707 1.489698 0.371379 -0.303441 -0.742302 -0.754928 0.488194 9: 3.578397 1.093266 1.409034 -0.225584 0.293871 -1.061582 1.370299 -0.177375 10: 2.769437 1.109273 1.417192 1.117356 -0.787283 2.350457 -1.711516 -0.196053 The Fourier coefficients Y: Col: 1 2 3 4 Row --- 1: 12.142966 -0.400139 1.426302 12.239901 6.872886 7.081277 4.529134 -10.685791 2: 4.408955 -4.457863 14.908230 0.334811 -2.067067 1.939489 14.505381 -12.041609 3: 4.436553 -5.895562 -10.244820 -9.320356 4.090992 -11.338965 -0.428533 -3.155948 4: -3.544900 0.162436 -1.592147 4.297108 11.221642 -2.749946 0.334760 5.934708 5: 5.114704 7.513746 -4.813562 -1.336493 -0.489492 0.663218 -14.513551 16.277058 6: -2.969651 -14.634894 -3.923796 -2.979124 2.516906 2.893651 -6.655623 8.728887 7: -2.571505 -13.557148 -8.627018 -12.975617 -4.303165 -3.797200 1.233800 13.019168 8: -3.890015 -6.805687 8.001171 -5.841650 0.928644 0.458107 -9.102910 -3.777936 9: -10.582258 -0.082497 -3.556199 -3.661382 -5.349990 8.459002 10.232335 8.307855 10: 4.931881 11.451995 9.564049 6.728195 3.285200 -0.729154 -3.953602 9.644652 The recovered data: Col: 1 2 3 4 Row --- 1: 0.537667 -0.102242 -1.349887 -0.863653 0.671497 -1.089064 0.888396 -0.615602 2: 1.833885 -0.241447 3.034923 0.077359 -1.207487 0.032557 -1.147070 0.748077 3: -2.258847 0.319207 0.725404 -1.214117 0.717239 0.552527 -1.068870 -0.192419 4: 0.862173 0.312859 -0.063055 -1.113501 1.630235 1.100610 -0.809499 0.888610 5: 0.318765 -0.864880 0.714743 -0.006849 0.488894 1.544212 -2.944284 -0.764849 6: -1.307688 -0.030051 -0.204966 1.532630 1.034693 0.085931 1.438380 -1.402269 7: -0.433592 -0.164879 -0.124144 -0.769666 0.726885 -1.491590 0.325191 -1.422376 8: 0.342624 0.627707 1.489698 0.371379 -0.303441 -0.742302 -0.754928 0.488194 9: 3.578397 1.093266 1.409034 -0.225584 0.293871 -1.061582 1.370299 -0.177375 10: 2.769437 1.109273 1.417192 1.117356 -0.787283 2.350457 -1.711516 -0.196053 c8vec_sft_test(): c8vec_sftf() computes the forward slow Fourier transform. c8vec_sftb() computes the backward slow Fourier transform. The number of data values, N = 36 The original data: 1 1.4193-0.36227i 2 0.29158+0.061141i 3 0.19781+0.21671i 4 1.5877-1.3981i 5 -0.80447+0.17887i 6 0.69662+0.92758i 7 0.83509-0.11018i 8 -0.24372+1.5724i ...... .............. .............. 36 0.12405+0.066869i The Fourier coefficients: 1 0.9134+1.4796i 2 0.5146+0.037389i 3 2.2244+1.6049i 4 4.7329+1.8513i 5 4.2936+3.3669i 6 6.5996-8.79012i 7 -2.0059+2.5728i 8 -8.89442+8.66193i ...... .............. .............. 36 11.7347-3.06621i The retrieved data: 1 1.4193-0.36227i 2 0.29158+0.061141i 3 0.19781+0.21671i 4 1.5877-1.3981i 5 -0.80447+0.17887i 6 0.69662+0.92758i 7 0.83509-0.11018i 8 -0.24372+1.5724i ...... .............. .............. 36 0.12405+0.066869i r8vec_sct_test(): r8vec_sct() does a forward or backward slow cosine transform. The number of data items is N = 256 The original data: 1 2.288769 2 3.611048 3 1.694996 4 2.006099 5 2.634899 6 4.471179 7 3.891803 8 0.346838 ...... .............. 256 2.586721 The cosine coefficients: 1 1323.449533 2 -16.540235 3 -10.508228 4 -23.582477 5 -29.736051 6 46.572491 7 57.353814 8 2.539218 ...... .............. 256 31.255790 The retrieved data: 1 2.288769 2 3.611048 3 1.694996 4 2.006099 5 2.634899 6 4.471179 7 3.891803 8 0.346838 ...... .............. 256 2.586721 r8vec_sft_test(): r8vec_sftf() computes the forward slow Fourier transform. r8vec_sftb() computes the backward slow Fourier transform. The number of data values, N = 36 The original data: 1 4.952556 2 1.132672 3 1.990026 4 3.482843 5 0.323204 6 3.738308 7 2.102002 8 4.056587 ...... .............. 36 4.691002 A (cosine) coefficients: 0 2.430824 1 0.430064 2 -0.094098 3 0.353495 4 0.350950 5 -0.100261 6 0.550932 7 -0.100902 8 0.289354 9 -0.360294 10 0.638934 11 -0.280434 12 -0.062729 13 0.048542 14 0.854362 15 0.172192 16 -0.059698 17 -0.140115 18 0.031437 B (sine) coefficients: 1 0.214492 2 -0.145524 3 -0.150529 4 -0.360150 5 -0.002669 6 -0.296374 7 -0.365227 8 0.579594 9 -0.852739 10 -0.371081 11 -0.244301 12 -0.145423 13 0.201740 14 -0.262526 15 -0.151835 16 0.608340 17 0.155489 18 0.000000 The retrieved data: 1 4.952556 2 1.132672 3 1.990026 4 3.482843 5 0.323204 6 3.738308 7 2.102002 8 4.056587 ...... .............. 36 4.691002 r8vec_sht_test(): r8vec_sht() does a forward or backward slow Hartley transform. The number of data items is N = 17 The original data: 1 3.102126 2 1.414200 3 1.025906 4 2.195670 5 0.136251 6 4.380922 7 3.050461 8 1.017962 ...... .............. 17 0.391144 The Hartley coefficients: 1 8.959794 2 -1.407646 3 -1.259832 4 1.041148 5 1.272548 6 0.558473 7 0.122569 8 3.307414 ...... .............. 17 0.055688 The retrieved data: 1 3.102126 2 1.414200 3 1.025906 4 2.195670 5 0.136251 6 4.380922 7 3.050461 8 1.017962 ...... .............. 17 0.391144 r8vec_sqct_test(): r8vec_sqctf() does a forward slow quarter wave cosine transform; r8vec_sqctb() does a backward slow quarter wave cosine transform. The number of data items is N = 256 The original data: 1 2.281754 2 0.239219 3 3.691285 4 0.190008 5 4.771222 6 3.711862 7 4.687248 8 2.566820 ...... .............. 256 2.734885 The cosine coefficients: 1 2.541386 2 -0.048859 3 -0.001696 4 -0.006446 5 0.075189 6 -0.106425 7 0.109871 8 -0.021567 ...... .............. 256 -0.030115 The retrieved data: 1 2.281754 2 0.239219 3 3.691285 4 0.190008 5 4.771222 6 3.711862 7 4.687248 8 2.566820 ...... .............. 256 2.734885 r8vec_sqst_test(): r8vec_sqstf() does a forward slow quarter wave sine transform; r8vec_sqstb() does a backward slow quarter wave sine transform. The number of data items is N = 256 The original data: 1 2.014850 2 0.535201 3 3.620831 4 3.068412 5 3.914841 6 2.833103 7 4.056596 8 2.883879 ...... .............. 256 0.691082 The sine coefficients: 1 -1.606357 2 -0.048369 3 -0.579920 4 -0.012354 5 -0.397669 6 -0.067263 7 -0.327497 8 -0.036480 ...... .............. 256 -0.017010 The retrieved data: 1 2.014850 2 0.535201 3 3.620831 4 3.068412 5 3.914841 6 2.833103 7 4.056596 8 2.883879 ...... .............. 256 0.691082 r8vec_sst_test(): r8vec_sst() does a forward or backward slow sine transform. The number of data items is N = 256 The original data: 1 4.315325 2 2.108732 3 2.056571 4 4.795707 5 3.751226 6 4.904986 7 1.167579 8 0.481134 ...... .............. 256 1.063795 The sine coefficients: 1 846.617617 2 -3.176464 3 269.743226 4 29.928347 5 178.739147 6 -36.672034 7 140.425576 8 2.308753 ...... .............. 256 8.971719 The retrieved data: 1 4.315325 2 2.108732 3 2.056571 4 4.795707 5 3.751226 6 4.904986 7 1.167579 8 0.481134 ...... .............. 256 1.063795 r8vec_swt_test(): r8vec_swtf() computes the forward slow wavelet transform. r8vec_swtb() computes the backward slow wavelet transform. The number of data values, N = 36 The original data: 1 0.408117 2 1.372397 3 4.337592 4 2.796785 5 2.323139 6 2.151505 7 3.869930 8 3.269602 ...... .............. 36 3.841676 I S(I) D(I) 1 1.955452 1.375397 2 4.676745 -1.917294 3 3.366062 0.283961 4 5.237050 -0.875280 5 2.419536 -1.128504 6 3.266492 0.017279 7 2.796461 0.435980 8 4.047245 1.225679 9 3.970473 1.204926 10 4.927273 0.795177 11 5.298396 -1.543951 12 4.018480 -2.063921 13 2.961930 -2.623762 14 2.005485 -1.235941 15 2.769258 -2.622226 16 1.795554 0.470612 17 2.400717 -2.065247 18 3.847368 1.295500 The retrieved data: 1 0.408117 2 1.372397 3 4.337592 4 2.796785 5 2.323139 6 2.151505 7 3.869930 8 3.269602 ...... .............. 36 3.841676 slow_fourier_transform_test(): Normal end of execution. 10-Nov-2026 14:19:51