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.

Author: johnrzaleski_eqbr0v

John R. Zaleski, PhD, CAP, CPHIMS, is Chief Analytics Officer of Bernoulli, a leader in real-time connected healthcare. Dr. Zaleski brings 21 years of experience in researching and ushering to market devices and products to improve healthcare. He received his PhD from the University of Pennsylvania, with a dissertation that describes a novel approach for modeling and prediction of post-operative respiratory behavior in post-surgical cardiac patients. Dr. Zaleski has a particular expertise in designing, developing, and implementing clinical and non-clinical point-of-care applications for hospital enterprises. Dr. Zaleski is the named inventor or co-inventor on seven issued patents related to medical device interoperability. He is the author of numerous peer-reviewed articles on clinical use of medical device data, information technology and medical devices and wrote three seminal books on integrating medical device data into electronic health records and the use of medical device data for clinical decision making, including the #1 best seller of HIMSS 2015 on connected medical devices.

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