(Nonperiodic Spline Filter) The filter equation for the nonperiodic spline filter is giv...

(Nonperiodic Spline Filter) The filter equation for the nonperiodic spline filter is given by the n × n system

Here the parameter α = 1/[2 sin(πΔx/λc)] involves measurement values of the profile, dimensions, andwavelength over a sampling interval. The solution w gives the profile values for the long wave components, and z –w are those for the short wave components. Use this system to test the Penta code using various values of α. Hint: For test systems, select a simple solution vector w = [1,−1, 1,−1, . . . , 1]T with a modest value for n, and then compute the right-hand side using matrix-vector multiplication z = (I + α⁴ Q)w.