Question

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 )

Answer #1

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 of the periodic function given on one
period of length 2 by
f(x) = x2, - 1 < x < 1:

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

1. Find the Fourier cosine series for f(x) = x on the interval 0
≤ x ≤ π in terms of cos(kx). Hint: Use the even extension.
2. Find the Fourier sine series for f(x) = x on the interval 0 ≤
x ≤ 1 in terms of sin(kπx). Hint: Use the odd extension.

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) =
{0, -pi < x < 0
{1, 0 <= x < pi

Find the Fourier Series of the function: f(x)=0, -5<x<0,
f(x)=3, 0<x<5 with a period=10.
Write briefly about how such a series expansion could be used?
For example, in digital to analog conversion?

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

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

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