08-Oct-2025 23:03:20 walsh_transform_test(): MATLAB/Octave version 6.4.0. Test walsh_transform() ffwt_test(): ffwt() computes a fast Walsh transform. I X(I) Y=FFWT(X)/N Z=FFWT(Y)/N 1 0.619377 0.585040 0.619377 2 0.940797 -0.029084 0.940797 3 0.483093 -0.014268 0.483093 4 0.283695 0.040053 0.283695 5 0.482950 0.044342 0.482950 6 0.327810 0.117227 0.327810 7 0.324676 -0.100337 0.324676 8 0.985249 0.137115 0.985249 9 0.697668 0.051584 0.697668 10 0.968356 -0.014722 0.968356 11 0.121633 -0.112105 0.121633 12 0.886121 -0.054961 0.886121 13 0.744601 -0.007060 0.744601 14 0.995680 0.054987 0.995680 15 0.105605 0.059158 0.105605 16 0.393327 -0.137590 0.393327 I X(I) Y=FFWT(X)/N Z=FFWT(Y)/N 1 1.000000 8.500000 1.000000 2 2.000000 -4.000000 2.000000 3 3.000000 0.000000 3.000000 4 4.000000 -2.000000 4.000000 5 5.000000 0.000000 5.000000 6 6.000000 0.000000 6.000000 7 7.000000 0.000000 7.000000 8 8.000000 -1.000000 8.000000 9 9.000000 0.000000 9.000000 10 10.000000 0.000000 10.000000 11 11.000000 0.000000 11.000000 12 12.000000 0.000000 12.000000 13 13.000000 0.000000 13.000000 14 14.000000 0.000000 14.000000 15 15.000000 0.000000 15.000000 16 16.000000 -0.500000 16.000000 fwt_test(): fwt() computes a fast Walsh transform. I X(I) Y=FWT(X)/N Z=FWT(Y)/N 1 0.897966 0.572499 0.897966 2 0.093704 -0.044807 0.093704 3 0.979512 0.090050 0.979512 4 0.918175 0.104597 0.918175 5 0.103397 -0.090575 0.103397 6 0.072376 0.099902 0.072376 7 0.179515 -0.090096 0.179515 8 0.976894 -0.145735 0.976894 9 0.520890 0.054730 0.520890 10 0.250587 0.141686 0.250587 11 0.923996 -0.071101 0.923996 12 0.831945 0.060417 0.831945 13 0.661429 0.089068 0.661429 14 0.813763 0.114927 0.813763 15 0.828703 -0.052022 0.828703 16 0.107139 0.064427 0.107139 I X(I) Y=FWT(X)/N Z=FWT(Y)/N 1 1.000000 8.500000 1.000000 2 2.000000 -4.000000 2.000000 3 3.000000 0.000000 3.000000 4 4.000000 -2.000000 4.000000 5 5.000000 0.000000 5.000000 6 6.000000 0.000000 6.000000 7 7.000000 0.000000 7.000000 8 8.000000 -1.000000 8.000000 9 9.000000 0.000000 9.000000 10 10.000000 0.000000 10.000000 11 11.000000 0.000000 11.000000 12 12.000000 0.000000 12.000000 13 13.000000 0.000000 13.000000 14 14.000000 0.000000 14.000000 15 15.000000 0.000000 15.000000 16 16.000000 -0.500000 16.000000 haar_test(): haar() computes a Haar transform. hnorm() normalizes the transformed data. haarin() computes an inverse Haar transform. I X(I) Y=HAAR(X) Z=HNORM(Y) W=HAARIN(Z) 1 0.338384 9.482272 0.592642 0.338384 2 0.878891 0.708145 0.044259 0.878891 3 0.941967 0.213632 0.026704 0.941967 4 0.495180 -0.202579 -0.025322 0.495180 5 0.582955 -0.219872 -0.054968 0.582955 6 0.662274 0.049671 0.012418 0.662274 7 0.968649 0.076861 0.019215 0.968649 8 0.226910 -1.254578 -0.313644 0.226910 9 0.527932 -0.540507 -0.270254 0.527932 10 0.556619 0.446787 0.223394 0.556619 11 0.839622 -0.079319 -0.039659 0.839622 12 0.168069 0.741739 0.370869 0.168069 13 0.167203 -0.028687 -0.014343 0.167203 14 0.352919 0.671553 0.335776 0.352919 15 0.976402 -0.185716 -0.092858 0.976402 16 0.798298 0.178104 0.089052 0.798298 I X(I) Y=HAAR(X) Z=HNORM(Y) W=HAARIN(Z) 1 1.000000 136.000000 8.500000 1.000000 2 2.000000 -64.000000 -4.000000 2.000000 3 3.000000 -16.000000 -2.000000 3.000000 4 4.000000 -16.000000 -2.000000 4.000000 5 5.000000 -4.000000 -1.000000 5.000000 6 6.000000 -4.000000 -1.000000 6.000000 7 7.000000 -4.000000 -1.000000 7.000000 8 8.000000 -4.000000 -1.000000 8.000000 9 9.000000 -1.000000 -0.500000 9.000000 10 10.000000 -1.000000 -0.500000 10.000000 11 11.000000 -1.000000 -0.500000 11.000000 12 12.000000 -1.000000 -0.500000 12.000000 13 13.000000 -1.000000 -0.500000 13.000000 14 14.000000 -1.000000 -0.500000 14.000000 15 15.000000 -1.000000 -0.500000 15.000000 16 16.000000 -1.000000 -0.500000 16.000000 walsh_test(): walsh() computes a fast Walsh transform. I X(I) Y=FWT(X)/N Z=FWT(Y)/N 1 0.330765 0.529022 0.330765 2 0.157237 -0.189769 0.157237 3 0.068120 -0.033530 0.068120 4 0.776095 0.027331 0.776095 5 0.115613 -0.007114 0.115613 6 0.017416 0.102057 0.017416 7 0.579744 -0.106253 0.579744 8 0.669037 -0.077742 0.669037 9 0.828262 0.054041 0.828262 10 0.569723 0.079583 0.569723 11 0.859425 -0.001935 0.859425 12 0.861203 0.088687 0.861203 13 0.678718 -0.017730 0.678718 14 0.912505 -0.050189 0.912505 15 0.635683 -0.048712 0.635683 16 0.404812 -0.016981 0.404812 I X(I) Y=FWT(X)/N Z=FWT(Y)/N 1 1.000000 8.500000 1.000000 2 2.000000 -4.000000 2.000000 3 3.000000 0.000000 3.000000 4 4.000000 -2.000000 4.000000 5 5.000000 0.000000 5.000000 6 6.000000 -0.000000 6.000000 7 7.000000 0.000000 7.000000 8 8.000000 -1.000000 8.000000 9 9.000000 0.000000 9.000000 10 10.000000 -0.000000 10.000000 11 11.000000 0.000000 11.000000 12 12.000000 -0.000000 12.000000 13 13.000000 0.000000 13.000000 14 14.000000 -0.000000 14.000000 15 15.000000 0.000000 15.000000 16 16.000000 -0.500000 16.000000 walsh_transform_test(): Normal end of execution. 08-Oct-2025 23:03:20