Laborator 3 SS
21
Laborator 3 SS Analiza semnalelor aperiodice cu ajutorul Transformatei Fourier Spectre de amplitudini si de faze 1. Generalitati: Transformata Fourier directa a unui semnal aperiodic este definita astfel: Transformata Fourier inversa este definita : Proprietati ale Transformatei Fourier folosite in acest laborator: a.) X(ω) este o functie continua, iar b.) Schimbarea de scara: c.) Teorema deplasarii in timp: Semnalele analizate in prezentul laborator sunt : 1. x(t) Cu cele doua cazuri : - x 1 (t), A>0 (A= +1) - x 2 (t), A<0 (A= -1) Page 1 of 21
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Transcript of Laborator 3 SS
Laborator 3 SSAnaliza semnalelor aperiodice cu ajutorul Transformatei Fourier
Spectre de amplitudini si de faze
1. Generalitati:
Transformata Fourier directa a unui semnal aperiodic este definita astfel:
Transformata Fourier inversa este definita :
Proprietati ale Transformatei Fourier folosite in acest laborator:
a.) X(ω) este o functie continua, iar
b.) Schimbarea de scara:
c.) Teorema deplasarii in timp:
Semnalele analizate in prezentul laborator sunt :
1. x(t)
Cu cele doua cazuri :- x1(t), A>0 (A= +1)- x2(t), A<0 (A= -1)
2. y(t)
Page 1 of 20
2. Analiza semnalului x(t) utilizand transformarea Fourier:
Se va construi schema electrica:
Semnalul generat de sursa de tensiune este x(t) (impuls dreptunghiular de latime τ
si amplitudine A)
Stiind ca transformata Fourier a lui x(t) este:
Sa se determine* spectrele de amplitudini si de faze( ),
spectrele de amplitudini ale partii reale si partii imaginare ( X(ω)=Re{X(ω)} + j Im{X(ω)}) si spectrul de energie pentru urmatoarele cazuri:
(2.1) A = 1 τ = 10m(2.2) A = 10 τ = 10m(2.3) A = 1 τ = 20m(2.4) A = -1 τ = 10m
Page 2 of 20
(2.5) A = -1 τ = 20m
Energia semnalului are urmatoarea expresie:
Folosindu-se valorile de la punctul (2.1) pentru A si τ se va lua pentru analiza si cazul (2.6) cu semnalul intarziat cu 20ms. Se vor determina cele 5 spectre si pentru cazul (2.6). Intarzierea semnalului se va realiza utilizand componenta IDEAL TIME DELAY
(2.7) I se va impune un prag de 4% (din valoarea amplitudinii pentru f=0) si in functie de acest prag se vor determina banda semnalului Bs si banda energetica Be. In Bs sau Be se vor regasi toate componentele cu aplitudinea mai mare decat 0.04Aτ
3. Se va analiza semnalul y(t) format din doua semnale x(t) (τ=10ms; A=1; T=20ms)
*Se va utiliza analiza: Analysis – Fourier Analysis – Fourier Spectrum unde se va tine cont de faptul ca functia sinc(ωτ/2) se anuleaza pentru f=k/τ
Cunascandu-se faptul ca transformata Fourier a unui tren de impulsuri dreptunghiulare (n impulsuri) este urmatoarea :
Page 3 of 20
Unde
si
Se vor determina cele 5 spectre (analog punctului 2) pentru semnalul y(t) format din doua impulsuri dreptunghiulare. Schema electrica va contine doua surse de semnal identice, circuitul de intarziere, o sursa de tensiune comandata in tensiune si doua rezistoare de sarcina.
4.Continutul referatului
4.1. Platforma de laborator (prezentul document)4.2. Schemele electrice si formele de unda ale semnalelor analizate (la punctele 2
si 3).4.3 Cerintele punctului 2 (2.1 – 2.7) precum si concluziile ce se pot desprinde la
analizarea spectrelor abtinute ( modificarile ce apar in spectre la modificarile survenite asupra amplitudinii, latimii impulsului si momentului de aparitie)
4.4. Cerintele punctului 3 (analog cu cerintele punctului 2)4.5. Concluzii generale (transformata Fourier si analiza spectrala)4.6. Data limita de predare/prezentare a referatului este data efectuarii lucrarii de
laborator nr. 4.
Exercitiul 2:
2.1
Page 4 of 20
T
Frequency (Hz)
0 500 1k 2k 2k
Am
plit
ud
e [V
/Hz]
0.00
25.00u
50.00u
75.00u
100.00u
T
Frequency (Hz)
0 1k 2k 3k
Ima
gin
ary
pa
rt [V
/Hz]
-7.00m
-6.00m
-5.00m
-4.00m
-3.00m
-2.00m
-1.00m
0.00
1.00m
T
Frequency (Hz)
0 500 1k 2k 2k
Re
al p
art
[V/H
z]
-10.00m
-5.00m
0.00
5.00m
10.00m
Page 5 of 20
T
Frequency (Hz)
0 1k 2k 3k
Ph
ase
[de
g]
-20.00k
-10.00k
0.00
10.00k
T
Frequency (Hz)
0 500 1k 2k 2k
Am
plit
ud
e [V
/Hz]
0.00
2.50m
5.00m
7.50m
10.00m
T
Time (s)
0.00 10.00m 20.00m 30.00m 40.00m
Vo
ltag
e (
V)
0.00
250.00m
500.00m
750.00m
1.00
Page 6 of 20
2.2 T
Frequency (Hz)
0 500 1k 2k 2k
Am
plit
ud
e [V
/Hz]
0.00
2.50m
5.00m
7.50m
10.00m
T
Frequency (Hz)
0 1k 2k 3k
Ima
gin
ary
pa
rt [V
/Hz]
-70.00m
-60.00m
-50.00m
-40.00m
-30.00m
-20.00m
-10.00m
0.00
10.00m
T
Frequency (Hz)
0 1k 2k 3k
Re
al p
art
[V/H
z]
-100.00m
-50.00m
0.00
50.00m
100.00m
Page 7 of 20
T
Frequency (Hz)
0 5k 10k 15k 20k
Ph
ase
[de
g]
-60.00k
-40.00k
-20.00k
0.00
T
Frequency (Hz)
0 1k 2k 3k 4k
Am
plit
ud
e [V
/Hz]
0.00
25.00m
50.00m
75.00m
100.00m
T
Time (s)
0.00 10.00m 20.00m 30.00m 40.00m
Vo
ltag
e (
V)
0.00
2.50
5.00
7.50
10.00
Page 8 of 20
2.3T
Frequency (Hz)
0 500 1k 2k 2k
Am
plit
ud
e [V
/Hz]
0.00
100.00u
200.00u
300.00u
400.00u
T
Frequency (Hz)
0 1k 2k 3k
Ima
gin
ary
pa
rt [V
/Hz]
-20.00m
-15.00m
-10.00m
-5.00m
0.00
T
Frequency (Hz)
0 50 100 150 200
Re
al p
art
[V/H
z]
-10.00m
0.00
10.00m
20.00m
Page 9 of 20
T
Frequency (Hz)
0 1k 2k 3k 4k
Ph
ase
[de
g]
-200.00
-150.00
-100.00
-50.00
0.00
T
Frequency (Hz)
0 1k 2k 3k
Am
plit
ud
e [V
/Hz]
0.00
5.00m
10.00m
15.00m
20.00m
T
Time (s)
0.00 10.00m 20.00m 30.00m 40.00m
Vo
ltag
e (
V)
0.00
250.00m
500.00m
750.00m
1.00
Page 10 of 20
2.4T
Frequency (Hz)
0 500 1k 2k 2k
Am
plit
ud
e [V
/Hz]
0.00
25.00u
50.00u
75.00u
100.00u
-spectrul de energie-
Page 11 of 20
T
Frequency (Hz)
0 1k 2k 3k 4k
Ima
gin
ary
pa
rt [V
/Hz]
-1.00m
0.00
1.00m
2.00m
3.00m
4.00m
5.00m
6.00m
7.00m
T
Frequency (Hz)
0 1k 2k 3k
Re
al p
art
[V/H
z]
-10.00m
-5.00m
0.00
5.00m
10.00m
T
Frequency (Hz)
0 1k 2k 3k 4k
Ph
ase
[de
g]
-50.00k
-40.00k
-30.00k
-20.00k
-10.00k
0.00
10.00k
Page 12 of 20
T
Frequency (Hz)
0 1k 2k 3k
Am
plit
ud
e [V
/Hz]
0.00
2.50m
5.00m
7.50m
10.00m
T
Time (s)
0.00 10.00m 20.00m 30.00m 40.00m
Vo
ltag
e (
V)
-1.00
-750.00m
-500.00m
-250.00m
0.00
2.5
Page 13 of 20
T
Frequency (Hz)
0 500 1k 2k 2k
Am
plit
ud
e [V
/Hz]
0.00
100.00u
200.00u
300.00u
400.00u
T
Frequency (Hz)
0 500 1k 2k 2k
Ima
gin
ary
pa
rt [V
/Hz]
0.00
5.00m
10.00m
15.00m
20.00m
T
Frequency (Hz)
0 50 100 150 200
Re
al p
art
[V/H
z]
-20.00m
-10.00m
0.00
10.00m
Page 14 of 20
T
Frequency (Hz)
0 1k 2k 3k 4k 5k
Ph
ase
[de
g]
0.00
50.00
100.00
150.00
200.00
T
Frequency (Hz)
0 1k 2k 3k
Am
plit
ud
e [V
/Hz]
0.00
5.00m
10.00m
15.00m
20.00m
T
Time (s)
0.00 10.00m 20.00m 30.00m 40.00m
Vo
ltag
e (
V)
-1.00
-750.00m
-500.00m
-250.00m
0.00
Page 15 of 20
2.6T
Frequency (Hz)
0 500 1k 2k 2k
Am
plit
ud
e [V
/Hz]
0.00
25.00u
50.00u
75.00u
100.00u
T
Frequency (Hz)
0 1k 2k 3k
Ima
gin
ary
pa
rt [V
/Hz]
-8.00m
-6.00m
-4.00m
-2.00m
0.00
2.00m
4.00m
6.00m
8.00m
T
Frequency (Hz)
0 1k 2k 3k
Re
al p
art
[V/H
z]
-10.00m
-5.00m
0.00
5.00m
10.00m
Page 16 of 20
T
Frequency (Hz)
0 1k 2k 3k
Ph
ase
[de
g]
0.00
50.00k
100.00k
150.00k
200.00k
T
Frequency (Hz)
0 500 1k 2k 2k
Am
plit
ud
e [V
/Hz]
0.00
2.50m
5.00m
7.50m
10.00m
T
Time (s)
0.00 10.00m 20.00m 30.00m 40.00m
Vo
ltag
e (
V)
0.00
250.00m
500.00m
750.00m
1.00
Page 17 of 20
Exercitiul 3:
T
Frequency (Hz)
0 1k 2k 3k 4k 5k
Imag
inar
y pa
rt [
V/H
z]
-20.00m
-10.00m
0.00
10.00m
T
Frequency (Hz)
0 1k 2k 3k 4k 5k
Imag
inar
y pa
rt [
V/H
z]
-20.00m
-10.00m
0.00
10.00m
Page 18 of 20
T
Frequency (Hz)
0 1k 2k 3k 4k 5k
Rea
l par
t [V
/Hz]
-10.00m
0.00
10.00m
20.00m
T
Frequency (Hz)
0 1k 2k 3k 4k 5k
Pha
se [
deg]
-5.00k
-4.00k
-3.00k
-2.00k
-1.00k
0.00
1.00k
2.00k
Page 19 of 20
T
Frequency (Hz)
0 1k 2k 3k 4k
Am
plitu
de [
V/H
z]
0.00
5.00m
10.00m
15.00m
20.00m
T
Time (s)
0.00 10.00m 20.00m 30.00m 40.00m
Vol
tage
(V
)
0.00
250.00m
500.00m
750.00m
1.00
Page 20 of 20
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