Why Smoothing kernels that sum to zero are always chosen

In Matlab. Analyze the rabbit growth rate problem using the transform Z. The following reference is suggested:https://la.mathworks.com/help/symbolic/compute-z-transforms-and-inverse-z-transformhtml

Last step in addition to the previous 2 questions: a lengthy derivation using phasors that the first diffraction peak should have an intensity of I1 ≈ 0.045 I0. Using the equation provided below in the pictures and the statement that β = 1.5π, you can find out what θ value to choose. You can also go for the midpoint between the first two destructive interference locations m = 1, 2 in the equation provided in the last question in which I will provide in the second image here. Repeat your three-path amplitude calculations for this value of θ, and observe what the relative intensity is for the first side maximum according to your calculation. Also explain How do the results improved when subdividing the aperture with 5, or 7, or more paths?

4. Identify the minterm expansion for L. 5. Give the most simplified Boolean expression for L, the output of the controller (LOCK) using the following Karnaugh map