What is the most lucid, intuitive explanation for the various FTs - CFT, DFT, DTFT and the Fourier Series?
I wrote this handout as a complement to Oppenheim and Willsky. Please take a look at Table 4.1 on page 14, reproduced below. (Click for larger image.) I wrote that table specifically to answer questions such as yours. 



Note the similarities and differences among the four operations:


"Series": periodic in time, discrete in frequency 
"Transform": aperiodic in time, continuous in frequency 
"Continuous Time": continuous in time, aperiodic in frequency 
"Discrete Time": discrete in time, periodic in frequency


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