404001 - Tín hi u và h th ng
Lecture-19
L y m u (Sampling)
Lý thuy t l y m u
Bi n i Fourier r i r c (DFT)
Bi n i Fourier nhanh (FFT)
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Lý thuy t l y m u
nh lý l y m u
Tín hi u có ph gi i h
khôi ph c chính xác t
ư cl y u nv it
Nói cách khác t n s l
Fs=2B Hz
n là B Hz có th
các m u c a nó
c
Fs>2B m u/s.
y m u nh nh t là
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
1
Lý thuy t l y m u
Xét tích c a chu i xung ơn v tu n hoàn δT(t) v i tín hi u f(t):
f (t ) = f (t )δ T (t )
∞
f (t ) = f (t ) ∑ δ (t − nT )
n =−∞
∞
f (t ) =
∑
f (nT )δ (t − nT )
n =−∞
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Lý thuy t l y m u
Ph c a tín hi u ư c l y m u:
f (t ) ↔ F (ω ) (Band-limited to B Hz)
2π ∞
δ T (t ) ↔ δ ωs (ω ) =
∑ δ (ω − nωs ) ; (Fs=1/T, ωs=2πFs)
T n =−∞
1
1 ∞
⇒ f (t )δ T (t ) ↔
[ F (ω ) ∗ δ ωs (ω )] = ∑ F (ω − nωs )
2π
T n=−∞
⇒ Fs ≥ 2 B or T ≤ 1/ 2 B
Fs = 2 B Nyquist rate
T = 1/ 2 B Nyquist int erval
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
2
Lý thuy t l y m u
Ví d : f (t ) = sin c 2 (5π t ) ư c l y m u v i các t n s khác nhau:
Fs=5Hz, 10Hz và 20Hz
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Lý thuy t l y m u
ωs
ωs
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
3
Lý thuy t l y m u
ωs
ωs
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Lý thuy t l y m u
Khôi ph c tín hi u
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
4
Lý thuy t l y m u
Khó khăn trong khôi ph c tín hi u th c t
Ideal Filter
Practical Filter
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
Lý thuy t l y m u
Aliasing effect
Gi i pháp: Anti-aliasing Filter
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10
5
nguon tai.lieu . vn