How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related?
Автор: Iain Explains Signals, Systems, and Digital Comms
Загружено: 2021-03-29
Просмотров: 127577
Explains how the Fourier Series (FS), Fourier Transform (FT), Discrete Time Fourier Transform (DTFT), Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT), Laplace Transform (LT) and Z-Transform (ZT) are all Related?
(* Note that for the DFT, unfortunately I forgot to say the last part of the explanation. I made the point that the DFT effectively assumes that the finite-length sampled signal is actually one period of an infinitely long periodic signal. I then drew the Fourier transform for the infinitely long discrete time signal. What I forgot to do, was to then say that the output of the DFT is only the finite part of that Fourier transform between omega=0 and omega=2pi. And that it is a discrete sequence with the same number of elements as the number of samples in the time domain sampled signal (and that the delta functions are finite). I fixed it on the summary sheet on my website: https://drive.google.com/file/d/1fh7T... . For more details see: "How does the Discrete Fourier Transform DFT relate to Real Frequencies?" • How does the Discrete Fourier Transform DF... )
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Related videos: (see http://www.iaincollings.com)
• Fourier Series and Eigen Functions of LTI Systems • Fourier Series and Eigen Functions of LTI ...
• What is the Fourier Transform? • What is the Fourier Transform? ("Brilliant...
• What is the Fourier Transform used for? • What is the Fourier Transform used for?
• Fourier Transform Equation Explained • Fourier Transform Equation Explained ("Bes...
• Typical Exam Question on Fourier Transform Properties • Typical Exam Question on Fourier Transform...
• Discrete Time Basis Functions • Discrete Time Basis Functions
• How does the Discrete Fourier Transform DFT relate to Real Frequencies? • How does the Discrete Fourier Transform DF...
• Laplace Transform Equation Explained • Laplace Transform Equation Explained
• Laplace Transform Region of Convergence Explained • Laplace Transform Region of Convergence Ex...
• What is the Z Transform? • What is the Z Transform?
• Z Transform Region of Convergence Explained • Z Transform Region of Convergence Explaine...
• Is Phase important in the Fourier Transform? • Is Phase important in the Fourier Transform?
For a full list of Videos and accompanying Summary Sheets, see the associated website: http://www.iaincollings.com
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