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Consider the function f(t) = {0, -pi <= t < 0, {t, 0 <= t < pi, with f(t) = f(t + 2). (a) Find the Fourier series for f(t).

Consider the function

f(t) =
{0, -pi <= t < 0,
{t, 0 <= t < pi,
with f(t) = f(t + 2).

(a) Find the Fourier series for f(t).
(b) Sketch the function to which the Fourier series of f(t) converges between t = 4*pi and t = 4.
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Math-8100410.pdf

Solutions 1. The fourier series of a function f(x) in the interval α &lt; x &lt; α + 2π is
given as


a0
f (x) =
+
an cos(nx) +
bn sin(nx)
(1)
2
n=1 n=1 where
α+2π a0 1
=
π f (x) dx
α...

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