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Aliasing and the Sampling Theorem Simplified

February 8, 2019 by 3200 Creative

Aliasing

In this lesson you will learn why aliasing occurs when sampling a signal. Aliasing is when a continuous-time sinusoid appears as a discrete-time sinusoid with multiple frequencies. The sampling theorem establishes conditions that prevent aliasing so that a continuous-time signal can be uniquely reconstructed from its samples. The sampling theorem is very important in signal processing. It tells us how fast we have to sample a signal with a given bandwidth to guarantee a unique correspondence between continuous- and discrete-time signals.

This lesson “simplifies” the sampling theorem because it only uses the non uniqueness of discrete-time sinusoids and the mapping between continuous- and discrete-time frequency. The next two lessons take a more conventional Fourier transform based approach to developing the sampling theorem.

Prerequisites

  • Introduction to Sampling and Reconstruction

Key Concepts and Screenshots

Concepts and Screenshots for Aliasing and the Sampling Theorem Simplified

Supplementary Material

Blog post on Aliasing in Movies

QuizzesStatus
1

Aliasing and the Sampling Theorem Simplified


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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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