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Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform

February 8, 2019 by 3200 Creative

The discrete Fourier transform is one of the most important computational tools in signal processing. This lesson briefly introduces you to some of the applications for the discrete Fourier transform, its definition, and develops the relationship between the discrete Fourier transform and the discrete-time Fourier transform. An understanding of this relationship is essential to proper use of the discrete Fourier transform in signal processing.

Prerequisites

  • The Four Fourier Representations

Key Concepts and Screenshots

Concepts and Screenshots for The Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform

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The Discrete Fourier Transform Sampling the Discrete Time Fourier Transform


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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

  • The Short-Time Fourier Transform and 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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