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

This video 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?
Related videos: (see http://www.iaincollings.com)
• Fourier Series and Eigen Functions of LTI Systems https://youtu.be/gRq3K4ZQKi8
• What is the Fourier Transform? https://youtu.be/G74t5az6PLo
• Fourier Transform Equation Explained https://youtu.be/8V6Hi-kP9EE
• Typical Exam Question on Fourier Transform Properties https://youtu.be/hPZ08BdjHL4
• Discrete Time Basis Functions https://youtu.be/P7q2YMQiat8
• How does the Discrete Fourier Transform DFT relate to Real Frequencies? https://youtu.be/pIFz84oj9cA
• Laplace Transform Equation Explained https://youtu.be/F_XmgIryugU
• Laplace Transform Region of Convergence Explained https://youtu.be/SexBL1OlhhU
• What is the Z Transform? https://youtu.be/n6MI-nEZoL0
• Z Transform Region of Convergence Explained https://youtu.be/uq_qv3Spzbs
• Is Phase important in the Fourier Transform? https://youtu.be/WyFO6yBQ0Cg

For a full list of Videos and accompanying Summary Sheets, see the associated website: http://www.iaincollings.com

(* 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. For more details see: https://youtu.be/pIFz84oj9cA)
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Видео How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related? канала Iain Explains Signals, Systems, and Digital Comms