7. Given a signal as the column vector x = (3.0 0.5 2.0 7.0)". The pyramid algorithm (for Haar wavelets) is as follows: The first two entries (3.0 0.5)T in the signal give an average of (3.0 + 0.5)/2 = 1.75 and a difference average of (3.0 – 0.5)/2 = 1.25. The second two entries (2.0 7.0) give an average of (2.0 + 7.0)/2 = 4.5 and a difference average of (2.0 – 7.0)/2 = -2.5. Thus we end up with a vector %3D (1.75 1.25 4.5 – 2.5)". Now we take the average of 1.75 and 4.5 providing (1.75 +4.5)/2 = 3.125 and the difference average (1.75 – 4.5)/2 = -1.375. Thus we end up with the vector y = (3.125 - 1.375 1.25 – 2.5)". (i) Find a 4 x 4 matrix A such that 3.0 3.125 0.5 -1.375 = Ay = A 2.0 1.25 7.0. -2.5 (ii) Show that the inverse of A exists. Then find the inverse.
7. Given a signal as the column vector x = (3.0 0.5 2.0 7.0)". The pyramid algorithm (for Haar wavelets) is as follows: The first two entries (3.0 0.5)T in the signal give an average of (3.0 + 0.5)/2 = 1.75 and a difference average of (3.0 – 0.5)/2 = 1.25. The second two entries (2.0 7.0) give an average of (2.0 + 7.0)/2 = 4.5 and a difference average of (2.0 – 7.0)/2 = -2.5. Thus we end up with a vector %3D (1.75 1.25 4.5 – 2.5)". Now we take the average of 1.75 and 4.5 providing (1.75 +4.5)/2 = 3.125 and the difference average (1.75 – 4.5)/2 = -1.375. Thus we end up with the vector y = (3.125 - 1.375 1.25 – 2.5)". (i) Find a 4 x 4 matrix A such that 3.0 3.125 0.5 -1.375 = Ay = A 2.0 1.25 7.0. -2.5 (ii) Show that the inverse of A exists. Then find the inverse.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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