Suppose the first few Fourier coeficients of some function f in C[0,2x] are ao, a1, a2, and b,, b2, b3. Which of the following trigonometric polynomials is closer to f? Defend your answer. ao +a, cost+a, cos 2t + b, sint g(t) = ao h(t) = +a, cost+a, cos 2t +b, sint+ b, sin 2t Choose the correct answer below. O A. The function h(t) is a better approximation because both functions are members of the space of trigonometric polynomials of order 2, and h(t) is the orthogonal projection of f onto that space. O B. The functions g(t) and h(t) are not members of the same space, and they are both orthogonal projections. It cannot be determined which function is closer to f. OC. The function g(t) is a better approximation because both functions are members of the space of trigonometric polynomials of order 2, and g(t) is an orthogonal projection that requires fewer terms to approximate f. O D. The function h(t) is a member of a higher order space than g(t) so it must be a closer approximation of f.

Suppose the first few Fourier coeficients of some function f in C[0,2x] are ao, a1, a2, and b,, b2, b3. Which of the following trigonometric polynomials is closer to f? Defend your answer. ao +a, cost+a, cos 2t + b, sint g(t) = ao h(t) = +a, cost+a, cos 2t +b, sint+ b, sin 2t Choose the correct answer below. O A. The function h(t) is a better approximation because both functions are members of the space of trigonometric polynomials of order 2, and h(t) is the orthogonal projection of f onto that space. O B. The functions g(t) and h(t) are not members of the same space, and they are both orthogonal projections. It cannot be determined which function is closer to f. OC. The function g(t) is a better approximation because both functions are members of the space of trigonometric polynomials of order 2, and g(t) is an orthogonal projection that requires fewer terms to approximate f. O D. The function h(t) is a member of a higher order space than g(t) so it must be a closer approximation of f.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

x+y 1-xy Q1. Prove that tan-x + tan-ly tan-
f Sin(mcso)= escrsim@) , thes the valke of 2晚 Gs (0+号) 10+4).
Differentiate the following hyperbolic functions.
Find differential operator that anni hilates 4e?x cos3x+3x? e°x a
Please create a word problem using the sinusoidal function attached
Find √ F SVE SVE ry sin(x² + y²) dedy 2 0 0 Calculator