MATH 416 Final: MATH416 BOYLE-M SPRING2015 0101 FINAL EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 416
• Professor: All

Document Summary

Don"t simplify your polynomial: (6 pts) for n 1, de ne cn(t) = 2 cos(2 nt), sn(t) = 2 sin(2 nt) and en(t) = e2 int. Which of the following modes of convergence hold? (no proof required. : convergence at every input x r, uniform convergence, convergence in l1(r), let dn be the determinant 1 matrix on indices {0, 1, . , n 1} which de nes the discrete fourier transform (dft). Let a be the smallest integer k such that h(k) 6= 0. Let b be the largest integer k such that h(k) 6= 0. 64p63: (a) (3 pts) let f = {x1, . Prove f spans cn. (b) (2 pts) exhibit a tight frame f of three vectors in r2. (c) (3 pts) let = e2 i/5. 2(cid:19) , (cid:18) 1 i 2(cid:19) , (cid:18) 1. Then < w, x >=< t (w), t (x) > for w, x in x.