Haar Wavelet Transform Calculation Primer

The DWT calculation is carried out in detail for a signal vector containing 8 data elements. The first step is to compute the averages and differences (divided by two) for each of the signal components. This is shown in Figures 1-4.

Figure 1
Figure 2
Figure 3
Figure 4

The next step involves computing the averages and differences of those averages and differences just computed. This is shown in Figures 5 and 6.

Figure 5
Figure 6

Finally, the last step involved is to compute the average and difference of the previous step. This is shown in Figure 7.

Figure 7

The discrete wavelet transform vector for the signal supplied is given by the bottom row, shown in Figure A-8. The color-coding is included to indicate where each of the computed differences (and the final average) is placed in the vector.

Figure 8

As the number of signal data points increases, so does the number of computations of averages and differences. This process lends itself quite readily to automation.