Исаев Ю.Н. Лекции по САУ
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91
92
Фурье анализ сигнала
93
Пример выполнении задания №1.
94
aT b 0
a
T2
3
b 1
solve
a
b
3
T
3
T 0.05
t 0 0.01 T
2T
2
T
f
1
T
ft()
t3
T
0t
T
3
if
1
T
3
t
2
3
Tif
1
t
T
3
T
3
2 t Tif
0 otherwise
0 0.017 0.033 0.05
0
0.2
0.4
0.6
0.8
1
1.2
ft()
t
M
5
k0M
a
k
2
T
0
T
t
ft( ) cos k t
d
a
1.333
0.456
0.113
0
0.028
0.018
A
k
ia
k
F t()
a
0
2
1
M
k
a
k
cos k t
F1 t()
A
0
2
1
M
k
A
k
sin k t arg A
k
0 0.05 0.1
0.6
1.2
Ft()
ft()
F1 t()
t
A
k
1.333
0.456
0.113
-5
5.636·10
0.028
0.018
arg A
k
deg
90
-90
-90
-90
-90
-90
95
Give
n
URC U'
C
Li'
L
E
CU'
C
i
L
Find i'
L
U'
C
URi
L
E
L
i
L
C
C
R
L
y=U
x=U
R
L 0.1
R 1
0
C 100 10
6
Et( ) F1 t()
A
R
L
1
C
1
L
0
Bt()
Et()
L
0
eigenvals A()
50 312.25i
50 312.25i
N 10
2
T 2T
1
Cp
pL R
float 5
solve p
50.( ) 312.24989991991991029i
50.( ) 312.24989991991991029i
i0
N
Dt x() Ax Bt()
x rkfixed
0
0
0 T N D
tx
0
96
0 0.02 0.04 0.06 0.08 0.1
0.15
0.1
0.05
0.05
0.1
0.15
x
1
10
x
0
0 0.02 0.04 0.06 0.08 0.1
0.25
0.25
0.5
0.75
1
1.25
x
2
x
0
W p( ) identity 2()p A()
1
1
L
0
Wp( ) float 4
10.00
p
p
2
100.0 p .1000e6
.1000e6
p
2
100.0 p .1000e6
o 2 4
T
A
Wi
0.01 1 10
3
97
0 200 400 600 800 1000
0.02
0.04
0.06
0.08
0.1
A ()
0
A o
0
0
A o
1
0
A o
2
0
o
0
o
1
o
2
0 200 400 600 800 1000
1.57
0.79
0.79
1.57
arg A ()
0
arg A o
0
0
arg A o
1
0
arg A o
2
0
o
0
o
1
o
2
0 200 400 600 800 1000
3.14
2.36
1.57
0.79
arg A ()
1
arg A o
0
1
arg A o
1
1
arg A o
2
1
o
0
o
1
o
2
0 200 400 600 800 1000
0.64
1.28
1.92
2.56
3.2
A ()
1
A o
0
1
A o
1
1
A o
2
1
o
0
o
1
o
2
F1 t()
A
0
2
A 0
0
1
M
k
A
k
A k
0
sin k t arg A
k
arg A k
0
F2 t()
A
0
2
A 0
1
1
M
k
A
k
A k
1
sin k t arg A
k
arg A k
1
0 0.02 0.04 0.06 0.08 0.1
0.25
0.25
0.5
0.75
1
1.25
F2 t
i
x
2
i
t
i
0 0.02 0.04 0.06 0.08 0.1
0.15
0.1
0.05
0.05
0.1
0.15
F1 t
i
R
x
1
i
R
t
i
Пример 2.
98
aT b 0
a
T
2
b 1
solve
a
b
2
T
2
T 0.0
5
t 0 0.01 T 2
T
2
T
f
1
T
ft()
t2
T
0t
T
2
if
1
t
T
2
T
2
t
T
if
0 otherwise
0 0.017 0.033 0.05
0
0.2
0.4
0.6
0.8
1
1.2
ft()
t
M
5
k0
M
a
k
2
T
0
T
t
ft( ) cos k t
d
a
1
0.405
0
0.045
0
0.016
A
k
ia
k
F t()
a
0
2
1
M
k
a
k
cos k t
F1 t()
A
0
2
1
M
k
A
k
sin k t arg A
k
0 0.05 0.1
0.6
1.2
Ft()
ft()
F1 t()
t
A
k
1
0.405
0
0.045
0
0.016
arg A
k
deg
90
-90
-90
-90
-90
-90
99
Give
n
URC U'
C
Li'
L
E
CU'
C
i
L
Find i'
L
U'
C
URi
L
E
L
i
L
C
C
x=U
C
R
L
y=U
L 0.
1
R 1
0
C 100 10
6
Et( ) F1 t()
A
R
L
1
C
1
L
0
Bt()
Et()
L
0
eigenvals A()
50 312.25i
50 312.25i
N 10
2
T 2
T
1
Cp
pL R
float 5
solve p
50.( ) 312.24989991991991029i
50.( ) 312.24989991991991029i
i0
N
Dt x
() Ax Bt()
x rkfixed
0
0
0 T N D
tx
0
100
0 0.02 0.04 0.06 0.08 0.1
0.25
0.25
0.5
0.75
1
1.25
x
2
x
0
0 0.02 0.04 0.06 0.08 0.1
0.1
0.05
0.05
0.1
x
1
10
x
0
W p( ) identity 2()p A()
1
1
L
0
Wp( ) float 4
10.00
p
p
2
100.0 p .1000e6
.1000e6
p
2
100.0 p .1000e6
o 2 4
T
A
Wi
0.01 1 10
3