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The DFT Approximation to the Fourier Transform

February 2, 2019 by 3200 Creative

The DFT Approximation to the Fourier Transform

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  1. Question 1 of 4
    1. Question

    Which of the following steps are involved in using the DFT to approximate the FT? Select all that apply.

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  2. Question 2 of 4
    2. Question

    Sampling the DFT at a dense set of frequencies reduces the error in approximating the FT that is introduced by truncating the signal in time.

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  3. Question 3 of 4
    3. Question

    The error introduced to the FT approximation due to sampling the signal in time can be reduced by increasing the sampling frequency.

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  4. Question 4 of 4
    4. Question

    Truncating the signal in the time domain makes the number of samples finite, but causes the underlying DTFT to be smeared by a sinc function.

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Course Lessons

  • Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform

  • Important Discrete Fourier Transform Properties

  • Fast Fourier Transform (FFT) Algorithm

  • Introduction to Circular Convolution and Filtering with the Discrete Fourier Transform

  • Circular Convolution Property of the Discrete Fourier Transform

  • Filtering with the Discrete Fourier Transform

  • The Discrete Fourier Transform Approximation to the Fourier Transform

  • The Effect of Windowing on the Discrete Fourier Transform Approximation to the Fourier Transform

  • Windows and the Discrete-Time Fourier Transform: Trading Resolution for Dynamic Range

  • An Example of Approximating the Fourier Transform with the Discrete Fourier Transform

  • Jupyter Notebook: Explore the Windowed DFT

  • The Short-Time Fourier Transform and the Spectrogram

  • Jupyter Notebook: Explore the Spectrogram

  • A Matrix Interpretation of the Discrete Fourier Transform

  • A Matrix Interpretation of the Fast Fourier Transform Algorithm

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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