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Sampling and Reconstruction

March 22, 2019 by 3200 Creative

All signals in the physical world, e.g., light, sound, seismic waves, and so on, have continuous independent variables.  These signals must be sampled to convert them to a sequence of numerical values prior to computer-based signal processing. The Sampling and Reconstruction series of 15 lessons introduces you to the requirements on sampling in order to ensure a unique representation.  You will learn to use the Fourier transform as a tool for analyzing the effect of sampling in the frequency domain.  Much of the series will teach you practical issues associated with sampling and techniques for addressing them, including anti-aliasing, oversampling, anti-imaging, upsampling and downsampling. Finally, you will learn how to model the apparent noise that is introduced when representing the amplitude of each sample with a finite number of bits.

Course Content

Lessons Status
1

Introduction to Sampling and Reconstruction

2

Aliasing and the Sampling Theorem Simplified

3

Fourier Transform Interpretation of Sampling

4

Reconstruction and the Sampling Theorem

5

Reconstruction and the Sampling Theorem Examples

6

Two-Dimensional Sampling Theorem

7

Equivalent Analog Filtering

8

Practical Sampling: Anti-Aliasing Filters

9

Practical Reconstruction: The Zero-Order Hold

10

Practical Digital Filtering and Oversampling

11

Oversampling Example

12

Downsampling: Reducing the Sampling Rate

13

Upsampling: Increasing the Sampling Rate

14

Analog to Digital Conversion: Quantization and Coding

15

Analysis of Quantization Error

Filed Under: Uncategorized

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Course Lessons

  • Introduction to Sampling and Reconstruction

  • Aliasing and the Sampling Theorem Simplified

  • Fourier Transform Interpretation of Sampling

  • Reconstruction and the Sampling Theorem

  • Reconstruction and the Sampling Theorem Examples

  • Two-Dimensional Sampling Theorem

  • Equivalent Analog Filtering

  • Practical Sampling: Anti-Aliasing Filters

  • Practical Reconstruction: The Zero-Order Hold

  • Practical Digital Filtering and Oversampling

  • Oversampling Example

  • Downsampling: Reducing the Sampling Rate

  • Upsampling: Increasing the Sampling Rate

  • Analog to Digital Conversion: Quantization and Coding

  • Analysis of Quantization Error

Courses

  • Foundations

  • Time Domain LTI Systems

  • Fourier Series and Transforms

  • Sampling and Reconstruction

  • The DFT and Applications

  • The Z-Transform

  • Intro to Filter Design

  • IIR Filter Design

  • FIR Filter Design

  • Random Signal Characterization

  • Basis Representations of Signals

  • Estimation of Power Spectra and Coherence

  • Introduction to Signal Estimation and Detection Theory

  • MMSE Filtering and Least-Squares Problems

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