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4.1 periodic sampling. 4.2 discrete-time processing of continuous-time signals. 4.3 continuous-time processing of discrete-time signal. 4.4 digital processing of analog signals. 4.5 changing the sampling rate using discrete-time processing. Chapter 4 sampling of continous-time signals.
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4.1 periodic sampling 4.2 discrete-time processing of continuous-time signals 4.3 continuous-time processing of discrete-time signal 4.4 digital processing of analog signals 4.5 changing the sampling rate using discrete-time processing Chapter 4 sampling of continous-time signals
4.1 periodic sampling1.ideal sample T:sample period fs=1/T:sample rate Ωs=2π/T:sample rate
Figure 4.1ideal continous-time-to-discrete-time(C/D)converter
time normalization tt/T=n Figure 4.2(a) mathematic model for ideal C/D
Figure 4.3 frequency spectrum change of ideal sample No aliasing aliasing aliasing frequency
Period =2πin time domain: w=2.1πand w=0.1πare the same trigonometric function property
high frequency is changed into low frequency in time domain:w=1.1π and w=0.9πare the same trigonometric function property
2.ideal reconstruction Figure 4.10(b) ideal D/C converter
ideal reconstruction in frequency domain Figure 4.4
Take sinusoidal signal for example to understand aliasing from frequency domain EXAMPLE Figure 4.5
EXAMPLE Sampling frequency:8Hz Reconstruct frequency:
EXAMPLE Figure 4.9
examples of sampling theorem(1) The highest frequency of analog signal ,which wav file with sampling rate 16kHz can show , is: 8kHz The higher sampling rate of audio files, the better fidelity.
examples of sampling theorem(2) according to what you know about the sampling rate of MP3 file,judge the sound we can feel frequency range( ) (A)20~44.1kHz (B)20~20kHz (C)20~4kHz (D)20~8kHz B
T=0.1; n=0:10; x=cos(10*pi*n*T); stem(n,x); dt=0.001; t=ones(11,1)* [0:dt:1]; n=n'*ones(1,1/dt+1); y=x*sinc((t-n*T)/T); hold on; plot(t/T,y,'r')
4.1 summary 1.representation in time domain of sampling
Requirements and difficulties: frequency spectrum chart of sampling and reconstruction comprehension and application of sampling theorem
Figure 4.11 4.2 discrete-time processing of continuous-time signals
Figure 4.12 conditions:LTI;no aliasing or aliasing occurred outside the pass band of filters EXAMPLE
EXAMPLE aliasing occurred outside the pass band of digital filters satisfies the equivalent relation of frequency response mentioned before. Figure 4.13
Figure 4.16 4.3 continuous-time processing of discrete-time signal
c Figure 4.12
EXAMPLE Ideal delay system:noninteger delay
quantization and coding Figure 4.41 4.4 digital processing of analog signals
Sampling and holding Figure 4.46(b)
uniform quantization and coding Figure 4.48
Figure 4.51 quantization error of 3BIT quantization error of8BIT
一维信号例子: index0 x 4 4 3 3 3 3 3 2 2 1 1 d(x,c0)=5 d(x,c1)=11 d(x,c2)=8 d(x,c3)=8 codewordc1 1 codeword c0 x 4 4 3 3 2 2 1 codewordc2 codewordc3 1 码书 vector quantization
Example: image coding • Initial image block(4 gray-levels,dimentions k=4×4=16) x 0 1 2 3 Code book C ={y0, y1 , y2, y3} y0 y1 y2 y3 codeword y1 is the most adjacent to x,so it is coded by the index “01”. d(x,y0)=25 d(x,y1)=5 d(x,y2)=25 d(x,y3)=46 vector quantization
reconstruction Figure 4.53 D/A过程