Bài giảng "Xử lý tín hiệu số: Sampling and Reconstruction" cung cấp cho người học các kiến thức: Introduction, review of analog signal, sampling theorem, analog reconstruction. Mời các bạn cùng tham khảo nội dung chi tiết.
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Nội dung Text: Bài giảng Xử lý tín hiệu số: Sampling and Reconstruction - Ngô Quốc Cường (ĐH Sư phạm Kỹ thuật)
- Xử lý tín hiệu số
Sampling and Reconstruction
Ngô Quốc Cường
ngoquoccuong175@gmail.com
Ngô Quốc Cường
sites.google.com/a/hcmute.edu.vn/ngoquoccuong
- Sampling and reconstruction
• Introduction
• Review of analog signal
• Sampling theorem
• Analog reconstruction
2
- 1.1 Introduction
Digital processing of analog signals proceeds in three
stages:
1. The analog signal is digitized, that is, it is sampled and each
sample quantized to a finite number of bits. This process is
called A/D conversion.
2. The digitized samples are processed by a digital signal
processor.
3. The resulting output samples may be converted back into
analog form by an analog reconstructor (D/A conversion).
3
- 1.2 Review of analog signal
• An analog signal is described by a function of time, say, x(t).
The Fourier transform X(Ω) of x(t) is the frequency spectrum
of the signal:
• The physical meaning of X(Ω) is brought out by the inverse
Fourier transform, which expresses the arbitrary signal x(t) as
a linear superposition of sinusoids of different frequencies:
4
- 1.2 Review of analog signal
• The response of a linear system to an input signal x(t):
• The system is characterized completely by the impulse
response function h(t). The output y(t) is obtained in the time
domain by convolution:
5
- 1.2 Review of analog signal
• In the frequency domain by multiplication:
• where H(Ω) is the frequency response of the system, defined
as the Fourier transform of the impulse response h(t):
6
- 1.2 Review of analog signal
7
- CT Fourier Transforms of Periodic Signals
Source: Jacob White 8
- Fourier Transform of Cosine
Source: Jacob White 9
- Impulse Train (Sampling Function)
Note: (period in t) T
(period in ) 2/T
Source: Jacob White 10
- 1.3 Sampling theorem
• The sampling process is illustrated in Fig. 1.3.1, where the
analog signal x(t) is periodically measured every T seconds.
Thus, time is discretized in units of the sampling interval T:
11
- 1.3 Sampling theorem
• For system design purposes, two questions must be
answered:
1. What is the effect of sampling on the original frequency
spectrum?
2. How should one choose the sampling interval T?
12
- 1.3 Sampling theorem
• Although the sampling process generates high frequency
components, these components appear in a very regular
fashion, that is, every frequency component of the original
signal is periodically replicated over the entire frequency axis,
with period given by the sampling rate:
• Let x(t) = xc(t), sampling pulse s(t)
13
- 1.3 Sampling theorem
Source: Zheng-Hua Tan 14
- 1.3 Sampling theorem
Source: Zheng-Hua Tan 15
- 1.3 Sampling theorem
Source: Zheng-Hua Tan 16
- 1.3 Sampling theorem
Source: Zheng-Hua Tan 17
- 1.3 Sampling theorem
Source: Zheng-Hua Tan
18
- 1.3 Sampling theorem
Source: Zheng-Hua Tan
19
- 1.3 Sampling theorem
• The sampling theorem provides a quantitative answer to the
question of how to choose the sampling time interval T.
• T must be small enough so that signal variations that occur
between samples are not lost. But how small is small
enough?
• It would be very impractical to choose T too small because
then there would be too many samples to be processed.
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