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Fourier Transform Interpretation of Sampling

February 2, 2019 by 3200 Creative

Fourier Transform Interpretation of Sampling

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  1. Question 1 of 3
    1. Question

    A continuous-time sinusoid of frequency 15 Hz is sampled at a rate of 60 samples per second. What is the frequency of the discrete-time sinusoid that results from sampling?

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  2. Question 2 of 3
    2. Question

    A discrete-time sinusoid of frequency \pi/2 rads was obtained by sampling a continuous-time sinusoid at intervals of 0.1 seconds. What was the frequency of the continuous-time sinusoid?

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  3. Question 3 of 3
    3. Question

    How is Fourier transform (FT) of the sampled signal related to the FT of the corresponding continuous-time signal? Assume the sampling interval is T seconds.

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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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