f(x) with an, bn defined by 0.5 0 -0.5 -1 -6 -4 -2 an = The standard definition of the Fourier Series representation of a periodic function f(x) with period L is given by: (²77″)], f(x)= ) = ² + 2 [²₂ a, cos (277) an f(x) = 0 2² 2 f(x) cos dr, b. - * f(z) sin (27Zn) dr. 2 bn L for all integer values of k {...-3,-2,-1,0,1,2,3,...}. Find the Fourier Series representation of f(x). 4 +b, sin 2πxn L Consider the periodic function f(x) with period L = 1 illustrated above and defined by: +1, for k≤ x
f(x) with an, bn defined by 0.5 0 -0.5 -1 -6 -4 -2 an = The standard definition of the Fourier Series representation of a periodic function f(x) with period L is given by: (²77″)], f(x)= ) = ² + 2 [²₂ a, cos (277) an f(x) = 0 2² 2 f(x) cos dr, b. - * f(z) sin (27Zn) dr. 2 bn L for all integer values of k {...-3,-2,-1,0,1,2,3,...}. Find the Fourier Series representation of f(x). 4 +b, sin 2πxn L Consider the periodic function f(x) with period L = 1 illustrated above and defined by: +1, for k≤ x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![6. Fourier Series
0.5
with an, bn defined by
-0.5
-1
an=
-4
The standard definition of the Fourier Series representation of a periodic function f(x) with period
L is given by:
bn =
-2
f(x) = +0, cos (2) + bu, ein (2)]
an
COS
n=1
f(x) =
0
2
2ππη
1/2 [ f(x) cos( d.x,
L
2ππη
26²
[ f(x) sin (²777)
for all integer values of k {...-3,-2,-1,0,1,2,3,...}.
Find the Fourier Series representation of f(x).
Consider the periodic function f(x) with period L = 1 illustrated above and defined by:
+1, for k≤x≤k+1/2
-1, for k+ 1/2 < x <k+1
dz.
(6)
(7a)
(7b)
(8)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F423822cb-5d3f-48f4-83a4-f0ba428ae79c%2F68a6a1bf-2e2a-4e48-b4dd-f6d8d7def29c%2Fia5imdh_processed.png&w=3840&q=75)
Transcribed Image Text:6. Fourier Series
0.5
with an, bn defined by
-0.5
-1
an=
-4
The standard definition of the Fourier Series representation of a periodic function f(x) with period
L is given by:
bn =
-2
f(x) = +0, cos (2) + bu, ein (2)]
an
COS
n=1
f(x) =
0
2
2ππη
1/2 [ f(x) cos( d.x,
L
2ππη
26²
[ f(x) sin (²777)
for all integer values of k {...-3,-2,-1,0,1,2,3,...}.
Find the Fourier Series representation of f(x).
Consider the periodic function f(x) with period L = 1 illustrated above and defined by:
+1, for k≤x≤k+1/2
-1, for k+ 1/2 < x <k+1
dz.
(6)
(7a)
(7b)
(8)
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