16-May-2025 11:12:16 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 0.936308 0.505821 0.936308 2 0.586411 -0.110498 0.586411 3 0.112291 0.039750 0.112291 4 0.045056 -0.015057 0.045056 5 0.638308 0.000656 0.638308 6 0.038723 0.186073 0.038723 7 0.473407 0.058627 0.473407 8 0.332082 0.095987 0.332082 9 0.548250 0.047553 0.548250 10 0.278658 0.045062 0.278658 11 0.776059 -0.026806 0.776059 12 0.643081 0.004857 0.643081 13 0.919947 -0.008879 0.919947 14 0.867862 -0.031593 0.867862 15 0.532736 0.033413 0.532736 16 0.363961 0.111342 0.363961 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 0.830166 0.401296 0.830166 2 0.003015 0.105602 0.003015 3 0.629722 0.062579 0.629722 4 0.944620 0.032403 0.944620 5 0.010832 -0.067251 0.010832 6 0.864000 -0.038143 0.864000 7 0.762136 0.048074 0.762136 8 0.010700 -0.127970 0.010700 9 0.028286 0.024953 0.028286 10 0.092444 -0.082773 0.092444 11 0.306915 0.192609 0.306915 12 0.634427 0.150722 0.634427 13 0.120965 0.065790 0.120965 14 0.236903 0.010958 0.236903 15 0.115611 0.102032 0.115611 16 0.830001 -0.050717 0.830001 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 0.849381 9.226170 0.576636 0.849381 2 0.694747 -0.089351 -0.005584 0.694747 3 0.707454 1.304938 0.163117 0.707454 4 0.685091 -0.882548 -0.110319 0.685091 5 0.213688 0.151583 0.037896 0.213688 6 0.393945 -0.416471 -0.104118 0.393945 7 0.493005 -1.031739 -0.257935 0.493005 8 0.531099 0.103264 0.025816 0.531099 9 0.397187 0.154634 0.077317 0.397187 10 0.030746 0.022363 0.011181 0.030746 11 0.505076 -0.180257 -0.090129 0.505076 12 0.954597 -0.038094 -0.019047 0.954597 13 0.765114 0.366441 0.183221 0.765114 14 0.671595 -0.449521 -0.224761 0.671595 15 0.507131 0.093519 0.046759 0.507131 16 0.826314 -0.319183 -0.159592 0.826314 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 0.718584 0.556155 0.718584 2 0.348158 -0.014519 0.348158 3 0.195137 0.087794 0.195137 4 0.997301 -0.064635 0.997301 5 0.972887 -0.057682 0.972887 6 0.182847 0.012275 0.182847 7 0.786798 0.025349 0.786798 8 0.131376 -0.011366 0.131376 9 0.125293 0.088095 0.125293 10 0.497855 0.075305 0.497855 11 0.341334 0.071943 0.341334 12 0.708497 0.057803 0.708497 13 0.863774 -0.183682 0.863774 14 0.648918 -0.050968 0.648918 15 0.743430 0.089466 0.743430 16 0.636293 0.037250 0.636293 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. 16-May-2025 11:12:16