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

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)
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• 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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