Industrieel ingenieur: 2e bachelor, 1e semester
Vak: Signalen en systemen - deel wiskunde III (Tonesi)
Hoofdstuk 6 - Fourrierreeksen
Op de powerpoint de uitgewerkte oefeningen vanuit de les
Geschreven oefeningen (voorbeelden)
1) domein : x 0 × = 0 is een punt van discontinuïteit
Isinxl
2)
y
is
begrensd : E 1
tuin ¥ ) er
# extrema !
3)
y
=
ten
¥ heeft oneindig f- En ,
¥)
'
y =
cost .
( Ez )
= E t)
x2
'
KIT
y
= 0
t =
Is +
-2 ( teken verandert)
'
kt 27 van
× =
y
IT t 2kt
oneindige extrema
voorbeeld 2
Bepaal de waarden vd .
F- reeks E (x ) horende bij flx) in de
punten met periode 6 .
X =
2,5
Ë
f (x ) = × 0 s × s 2 X = 4
ze × s 3 X = 0
103
?
X =
× = -
as
<
)
8 A
af
• : Interieurzijnarmaturen
-
voldoen
4 - .
. vigerend
-
✓ -
periode : 2L = 6 -
extrema
0 = 6
1
t 3 6
-
s _
→ als niet op tekening (vb 103 )
, '
•
E ( 2,5 ) = E
( Ez ) =
III ) =
# =
In
•
E ( 4) =
21 ( f (4) +
flut) ) =
t (1+1-11)=0
•
E ( 103) = E ( 1 -1102 ) = E ( 1) =
f (1) = 1
6. 17
•
E C- 39 ) = E ( 42 -
39 ) =
E (3) =
¥ ( f 137
+
f 134) =
t (32-11) = 5
extrema
•
E (o ) t ( f 10) t
f ( 6 )) t ( o + C- nl
) =
f
-
= =
voorbeeld 3
Bepaal de Fourierreeks horende bij fix) met
periode zit
flx )
{¥
= -
IT a × s 0
0 < X C IT
•
2 L =
2T = ) L = IT
•
do =
t lab fix) dx =
¥ f! ook +
f- ff x da
=
¥ 1:
II
¥
=
.
2
= IT
I
am =
f ja fix ) cost da =
¥ [ 9kt -
ios
(
k
) en
= 0 +
¥ { x. Cos ( Kx) dx
PE
fx .
costtax) on
ga nii Kx -
f t sein ( Kx) de Index
'
Kx sink
D- I
g Cos
9 ¥
= =
.
sein ( Kx) I Kx
'
f f
t cd
=
+ + C = × = 1
H2
ak =
¥ [¥ seinen +
In casu
]
¥ [En sine)
t coski )
Lotte ) )
= + -
0 Vk = 1
¥ [ La coski
t)
= -
=
In te +
cost [ treuren
=
¥ ,
( -
-
en + C- 1)k )
{
o
2
er even
er oneven
= . -
(-2 )
# ( 2k + 1) 2
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