Question

Find the Fourier series of the periodic function given on one period of length 2 by

f(x) = x^{2}, - 1 < x < 1:

Answer #1

Find the Fourier series of f(x) as given over one period.
1.
f(x) =(0 if −2 < x < 0 and
2 if 0 < x < 2 )

Fourier Series
Expand each function into its cosine series and sine series for
the given period
P=2
f(x) = x, 0<=x<5
f(x) = 1, 5<=x<10

The sketch of the following periodic function f(t)
given in one period,
f(t) = {(3t+1), -1 < t <= 1 and
0, -3 < t <= -1
a) Find period of the function, 2p?
b) Find Fourier coeff, a0, an (n
=>1), bn?
c) Fourier series representation of f(t)?
d) Result from (c), find the
first four non-zero term?

Fourier Series Expand each function into its cosine series and
sine series for the given period P = 2π f(x) = cos x

Find the Fourier cosine series and sine series, respectively,
for the even and odd periodic extensions of the following function:
f(x)= x if 0<x<π/2.
2 if π/2<x<π.
Graph f with its periodic extensions (up to n = 4) using
Mathematica.(leave codes here)

Find the fourier series representation of each periodic
function
f(x) = 0, -4 <x<0
f(x) = 8, 0<=x<=1
f(x) = 0, 1<x<4

Find the Fourier series for the following function (which has
period 2): f(x)= −x if −1<x<0
x if 0 < x < 1

Find the Fourier series for the following function (which has
period 4): f(x) = −x−2 if −2<x<0
−x + 2 if 0 < x < 2

Find the Fourier series of the function f(x) = |x|, −π/2 < x
< π/2 , with period π.

Find the Fourier series of the function f on the given
interval.
f(x) =
0,
−π < x < 0
1,
0 ≤ x < π

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