文档介绍：Chapter4 Digital Processing of Continuous-Time Signals
Sampling of Continuous-Time Signals
Recovery of the Analog Signal
Implication of the Sampling Process
Sampling of Bandpass Signals
Analog Lowpass Filter Design
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Introduction
The Basic Framework of a DSP System
-filter:get rid of the ponents we don’t interested in.—Anti-aliasing filter.
:transform analog signal into digital signal.
:process the digital signal.
:to transform digital signal into analog ones.
filter:filter the high frequency that is needless.—Reconstruction filter.
Pre-filter
AD
DSP
Analog
filter
x[n]
y[n]
DA
S/H
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Introduction
A simplified representation of DSP system:
We will use this figure to represent the working principle of this system.
Ideal Sampler
Discrete Time Processor
Ideal Interpolator
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Sampling of Continuous-Time Signals
(a)
(b)
Ideal sampling models
t
0
t
0
t
0
T
t
0
t
0
t
0
T
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Effect of Sampling in the Frequency Domain
When τ«T, p(t) ~δT(t),so firstly to discuss ideal sampling:
The output of ideal sampling is:
(1)In time domain:
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Effect of Sampling in the Frequency Domain
(2)In frequency domain:
If given:
We can get:
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Effect of Sampling in the Frequency Domain
The frequency procedure of sampling
0
…
0
…
0
…
…
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Sampling Theorem-(Nyquist Theorem)
Assume ga(t) is a band-limited signal with a CTFT Ga(j) as shown below:
The spectrum P(j) of p(t) having a sampling period T=2/T is indicated below:
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Sampling Theorem-(Nyquist Theorem)
Two possible spectra of Gp(j) are shown below:
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Sampling Theorem-(Nyquist Theorem)
From above discussion, we can see:
(1)If ga(t) is bandlimited with
(2)If
Please look at P175 .(a)(b)(c)
We call the frequency Ωs/2 which satisfies condition(2) is Nyquist frequency or folding frequency, and (2) is called Nyquist condition.
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