MA 3065 Midterm: hw5_sol

• School: Minneapolis College of Art and Design
• Department: Filmmaking-Sound
• Course: MA 3065
• Professor: p

Document Summary

Math 5588 homework 5 solutions: properties of the convolution. The fourier transform of u is bu(k) = e k2/2, so by the fourier convolution theorem. Choosing a = 2 we have and so. = f(u u). (u u)(x) = e x2/4: find the fourier transform of the box function u(x) =(1, 0, if |x| < 1 if |x| > 1. The fourier transform is given by bu(k) = Taking fourier transfomrs in x on both sides yields withbu(k, 0) = bf (k). For u the box function from problem 3 and. 1 sin2 x x2 dx = . sin2 x x2 dx dx = 2: nyquist-shannon sampling theorem: let f be an integrable function whose fourier transform bf vanishes outside of ( , )1. 1this means bf (k) = 0 for |k| . (cid:1) e in k/ f(cid:0) n for k . (1) (a) show that when . Simplify the coe cients with the inverse fourier transform formula.