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Fourier Transform Interpretation of Sampling

February 8, 2019 by 3200 Creative

fourier-transform-sampling

In the Fourier Transform Interpretation of Sampling lesson you will learn how the Fourier transform of the sampled signal depends on the Fourier transform of the original continuous-time signal. This relationship provides the basis for understanding the sampling theorem, how to reconstruct a continuous-time signal from samples, and how aliasing can distort the frequency content of the sampled signal.

This lesson provides a step-by-step derivation of this relationship using properties of the Fourier transform and complements the more intuitive development in the preceding lesson.

Prerequisites

  • Introduction to Sampling and Reconstruction

Key Concepts and Screenshots

Concepts and Screenshots for Fourier Transform Interpretation of Sampling

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Fourier Transform Interpretation of Sampling


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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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