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Spring 2012
Signals and Systems
Chapter SS-7Sampling
Shou shui Wei
Sep08 – Dec08
Figures and images used in these lecture notes are adopted from“Signals & Systems” by Alan V. Oppenheim and Alan S. Willsky, 1997
Shou shui Wei©2012Outline
Representation of of a Continuous-Time Signal
by Its Samples: The Sampling Theorem
Reconstruction of of a Signal from Its Samples
Using Interpolation
The Effect of Under-sampling: Aliasing
Discrete-Time Processing of Continuous-Time
Signals
Sampling of Discrete-Time Signals
SDU-BME
Shou shui Wei©2012The Sampling Theorem
Representation of CT Signals by its Samples
Shou shui Wei©2012The Sampling Theorem
Representation of CT Signals by its Samples
Shou shui Wei©2012The Sampling Theorem
Representation of CT Signals by its Samples
Shou shui Wei©2012The Sampling Theorem
Impulse-Train Sampling:
Shou shui Wei©2012The Sampling Theorem
Impulse-Train Sampling:
Ex 4.8, pp. 299-300
Eq 4.70, p. 322
Ex 4.21, p. 323
Shou shui Wei©2012The Sampling Theorem
Impulse-Train Sampling: Ex 4.21, 4.22, pp. 323-4
Shou shui Wei©2012The Sampling Theorem
The Sampling Theorem:
Shou shui Wei©2012The Sampling Theorem
Exact Recovery by an Ideal Lowpass Filter:
Shou shui Wei©2012The Sampling Theorem
Sampling with Zero-Order Hold:
Shou shui Wei©2012The Sampling Theorem
Sampling with Zero-Order Hold:Ex 4.4, p. 293
Eq 4.27, p. 301
Shou shui Wei©2012Outline
Representation of of a Continuous-Time Signal
by Its Samples: The Sampling Theorem
Reconstruction of of a Signal from Its Samples
Using Interpolation
The Effect of Under-sampling: Aliasing
Discrete-Time Processing of Continuous-Time
Signals
Sampling of Discrete-Time Signals
Shou shui Wei©2012Reconstruction of a Signal from its Samples Using Interpolation
Exact Interpolation:
Ex 2.11, p. 110
Shou shui Wei©2012Reconstruction of a Signal from its Samples Using Interpolation
Exact Interpolation:
Shou shui Wei©2012Reconstruction of a Signal from its Samples Using Interpolation
Ideal Interpolating Filter & The Zero-Order Hold:
Shou shui Wei©2012Reconstruction of a Signal from its Samples Using Interpolation
Sampling & Interpolation of Images:
Shou shui Wei©2012Reconstruction of a Signal from its Samples Using Interpolation
Higher-Order Holds:
Shou shui Wei©2012Reconstruction of a Signal from its Samples Using Interpolation
Higher-Order Holds:
= *
=
Ex 4.4, p. 293
X
Shou shui Wei©2012Reconstruction of a Signal from its Samples Using Interpolation
First-Order Hold on Image Processing:
Shou shui Wei©2012Outline
Representation of of a Continuous-Time Signal
by Its Samples: The Sampling Theorem
Reconstruction of of a Signal from Its Samples
Using Interpolation
The Effect of Under-sampling: Aliasing
Discrete-Time Processing of Continuous-Time
Signals
Sampling of Discrete-Time Signals
Shou shui Wei©2012Effect of Under-sampling: Aliasing
Overlapping in Frequency-Domain: Aliasing
Shou shui Wei©2012Effect of Under-sampling: Aliasing
Overlapping in Frequency-Domain: Aliasing
Shou shui Wei©2012Effect of Under-sampling: Aliasing
Overlapping in Frequency-Domain: Aliasing
Shou shui Wei©2012Effect of Under-sampling: Aliasing
Overlapping in Frequency-Domain: Aliasing
Shou shui Wei©2012Effect of Under-sampling: Aliasing
Overlapping in Frequency-Domain: Aliasing
Shou shui Wei©2012Effect of Under-sampling: Aliasing
Overlapping in Frequency-Domain: Aliasing
Shou shui Wei©2012Effect of Under-sampling: Aliasing
Overlapping in Frequency-Domain: Aliasing
Shou shui Wei©2012Effect of Under-sampling: Aliasing
Strobe Effect:
Shou shui Wei©2012Outline
Representation of of a Continuous-Time Signal
by Its Samples: The Sampling Theorem
Reconstruction of of a Signal from Its Samples
Using Interpolation
The Effect of Under-sampling: Aliasing
Discrete-Time Processing of Continuous-Time
Signals
Sampling of Discrete-Time Signals
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
Discrete-Time Processing of CT Signals:
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
C/D or A-to-D (ADC) and D/C or D-to-A (DAC):
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
C/D Conversion:
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
C/D Conversion:
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
C/D Conversion:
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
C/D Conversion:
Table 4.2, p. 329 Eq 7.3, 7.6, p. 517
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
D/C Conversion:
Overall System:
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
Frequency-Domain Illustration: 1
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
Frequency-Domain Illustration:
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
CT & DT Frequency Responses:
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
Digital Differentiator:Ex 4.16, p. 317
Shou shui Wei©2012Discrete-Time Processing of Continuous-Time Signals
Half-Sample Delay:Ex 4.15, p. 317
Shou shui Wei©2012Outline
Representation of of a Continuous-Time Signal
by Its Samples: The Sampling Theorem
Reconstruction of of a Signal from Its Samples
Using Interpolation
The Effect of Undersampling: Aliasing
Discrete-Time Processing of Continuous-Time
Signals
Sampling of Discrete-Time Signals
Shou shui Wei©2012Sampling of Discrete-Time Signals
Impulse-Train Sampling:
Shou shui Wei©2012Sampling of Discrete-Time Signals
Impulse-Train Sampling:
Shou shui Wei©2012Sampling of Discrete-Time Signals
Exact Recovery Using Ideal Lowpass Filter:
Shou shui Wei©2012Sampling of Discrete-Time Signals
DT Decimation & Interpolation: Down-samplingEq 5.45, p. 378: Time expansion
Shou shui Wei©2012Sampling of Discrete-Time Signals
Higher Equivalent Sampling Rate: Up-sampling
Shou shui Wei©2012Sampling of Discrete-Time Signals
Down-sampling
+ Up-sampling:
Shou shui Wei©2012In Summary
Shou shui Wei©2012In Summary
Discrete-Time Processing of CT Signals
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