Linear Algebra and Its Applications · Problem 3.4.23

Orthogonality — Gilbert Strang

Mathematics · fourier-coefficients-step-function

Problem

Find the Fourier coefficients

a_0

a_1

b_1

of the step function

y(x)

, which equals 1 on the interval

0 \leq x \leq \pi

and 0 on the remaining interval

\pi < x < 2\pi

a_0 = \frac{(y, 1)}{(1, 1)} \qquad a_1 = \frac{(y, \cos x)}{(\cos x, \cos x)} \qquad b_1 = \frac{(y, \sin x)}{(\sin x, \sin x)}.