How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related?

Описание: 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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