You are given a vector of numbers: [127, 71, 87, 31, 59, 3, 43, 99, 100, 42, 0, 58, 30, 88, 72, 130], each data point records the frequency of communication of a server in a 5-minute interval. For example, in the first 5 minutes, 127 contacts are observed. In the next 5 minutes, 71 contacts, … Required:

a. Give the Haar decomposition and draw a corresponding error tree for the contacts data vector.

b. Give the process and result for reconstructing the frequency during time interval [15, 20] using Haar decomposition.

c. Use Haar decomposition and error tree to compute the total number of communications between time interval [15, 30].