Electrical Engineering University of Technology-Irag 2 year. Math. 4 Example: Use complex form, find the Fourier series of the function Solution: 2π To= 27, wo= wo 1 To 1 f(t)e-indt [] C₁=7 (-1) e-int dt+ (1) e-int 2π i + C₁₁ 2лn -m i ⇒ C₁₁ = [(-1)"-1] πη i [(-1)"-1 lent TN 1 4 2T -in -in The complex exponential Fourier series, f(t) = - Σ Cent ⇒C₁ TY Dr. Jasim Farhood Hussein (-1 -≤ISO 0≤t≤n int f(t) = 1 + [ (1) the d + e DO = f(0) = [ 31-00 11=-8 H.W.: Find the exponential Fourier series for the following functions. 1/(t) = sint ↑(1) - p² МАЙ M. AMA -2x 49

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Electrical Engineering
University of Technology-Irag
2 year. Math. 4
Example: Use complex form, find the Fourier series of the function
Solution:
2π
To 2π, wo=
=
-
wo 1
=
To
f(t)e-indt
C₁=7
#{1+²+
2π
-17
1
e
i
⇒C₁=
2π -in
⇒C₁ =
-in
2лn
-#
-71
i
⇒ C₁ = [(-1)"-1]
πη
The complex exponential Fourier series,
DO
i
f(t) = [
Σ
-£-
= f(0) = [ [(-1)"-1 lent
Cent
TEN
310-8
11=48
H.W.: Find the exponential Fourier series for the following functions.
1/(t)=sint
↑(1)-1²
mm. Ans.
m₂
AMA
2л
-2x
***
44
۱۳
+
e
TY
Dr. Jasim Farhood Hussein
-≤I≤0
f(0) = (1 OSIST
-int dt
=>₁=
int
(-1) e-int dt+ (1) e-int
+ e
int
C
Transcribed Image Text:Electrical Engineering University of Technology-Irag 2 year. Math. 4 Example: Use complex form, find the Fourier series of the function Solution: 2π To 2π, wo= = - wo 1 = To f(t)e-indt C₁=7 #{1+²+ 2π -17 1 e i ⇒C₁= 2π -in ⇒C₁ = -in 2лn -# -71 i ⇒ C₁ = [(-1)"-1] πη The complex exponential Fourier series, DO i f(t) = [ Σ -£- = f(0) = [ [(-1)"-1 lent Cent TEN 310-8 11=48 H.W.: Find the exponential Fourier series for the following functions. 1/(t)=sint ↑(1)-1² mm. Ans. m₂ AMA 2л -2x *** 44 ۱۳ + e TY Dr. Jasim Farhood Hussein -≤I≤0 f(0) = (1 OSIST -int dt =>₁= int (-1) e-int dt+ (1) e-int + e int C
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