22-Apr-2023 17:37:14 walsh_transform_test(): MATLAB/Octave version 5.2.0. Test walsh_transform() ffwt_test(): ffwt() computes a fast Walsh transform. I X(I) Y=FFWT(X)/N Z=FFWT(Y)/N 1 0.761115 0.488456 0.761115 2 0.791264 0.108868 0.791264 3 0.785739 0.093401 0.785739 4 0.380911 -0.010968 0.380911 5 0.823934 0.023282 0.823934 6 0.645569 -0.084997 0.645569 7 0.141853 0.128507 0.141853 8 0.448205 0.029640 0.448205 9 0.068317 -0.056362 0.068317 10 0.500945 0.062579 0.500945 11 0.375386 -0.035478 0.375386 12 0.156228 -0.079484 0.156228 13 0.102576 0.042899 0.102576 14 0.451045 0.019934 0.451045 15 0.666740 0.053585 0.666740 16 0.715466 -0.022748 0.715466 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 0.186676 0.589059 0.186676 2 0.993927 -0.085695 0.993927 3 0.846361 0.079521 0.846361 4 0.255078 -0.012375 0.255078 5 0.247596 0.103130 0.247596 6 0.109067 0.035709 0.109067 7 0.410464 -0.025723 0.410464 8 0.977748 -0.093325 0.977748 9 0.661074 -0.031622 0.661074 10 0.504279 -0.054968 0.504279 11 0.312943 -0.206972 0.312943 12 0.853131 -0.056072 0.853131 13 0.434363 0.006765 0.434363 14 0.828893 0.019834 0.828893 15 0.959516 0.001095 0.959516 16 0.843831 -0.081685 0.843831 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 0.933548 9.811457 0.613216 0.933548 2 0.766269 3.439488 0.214968 0.766269 3 0.773713 0.249721 0.031215 0.773713 4 0.964066 -0.890720 -0.111340 0.964066 5 0.688331 -0.037962 -0.009491 0.688331 6 0.924340 0.037467 0.009367 0.924340 7 0.970252 -0.483263 -0.120816 0.970252 8 0.604952 0.220040 0.055010 0.604952 9 0.174232 0.167279 0.083640 0.174232 10 0.157952 -0.190352 -0.095176 0.157952 11 0.417172 -0.236009 -0.118004 0.417172 12 0.398276 0.365300 0.182650 0.398276 13 0.795574 0.016280 0.008140 0.795574 14 0.333622 0.018896 0.009448 0.333622 15 0.475932 0.461952 0.230976 0.475932 16 0.433225 0.042707 0.021353 0.433225 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 0.802162 0.508139 0.802162 2 0.332084 0.055059 0.332084 3 0.985295 -0.130639 0.985295 4 0.025884 0.103798 0.025884 5 0.956418 -0.090311 0.956418 6 0.517625 0.032203 0.517625 7 0.023839 0.060509 0.023839 8 0.862273 0.028366 0.862273 9 0.256478 0.027881 0.256478 10 0.809241 0.070606 0.809241 11 0.768407 -0.081119 0.768407 12 0.915942 -0.139701 0.915942 13 0.270716 0.084091 0.270716 14 0.347312 0.144550 0.347312 15 0.058260 0.121673 0.058260 16 0.198283 0.007058 0.198283 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. 22-Apr-2023 17:37:14