CSIR NET Dec 2015 Q101: Geophysics

The total energy of a discrete signal or wavelet is defined as the sum of the squared magnitudes of its samples: E = sum |x_n|^2. For a complex sample a+bi, |a+bi|^2 = a^2+b^2. For the wavelet (2+i, 1+i, i, i-1, i-2): |2+i|^2 = 4+1 = 5; |1+i|^2 = 1+1 = 2; |i|^2 = 0+1 = 1; |i-1|^2 = |-1+i|^2 = 1+1 = 2; |i-2|^2 = |-2+i|^2 = 4+1 = 5. Summing: 5+2+1+2+5 = 15, matching option 4.

Option 1 (1+5i) and option 2 (5+i) are complex-valued results, but total energy (a sum of squared magnitudes) must be a real, non-negative number, so these cannot represent a valid energy calculation. Option 3 (1) corresponds to only the |i|^2 term of the wavelet, omitting the other four samples' contributions. Option 4 is correct: summing |a+bi|^2 for all five complex samples gives exactly 5+2+1+2+5 = 15.