I am trying to make a succinct summary of how algebraic operations in the time domain translate in the frequency domain (via the use of Fourrier/Laplace transforms). Here is what I have derived so far:
Time Domain Frequency Domain
Time Delay Frequency shift
However, I have noticed that if summation/superposition is the same in time and frequency domain, how can multiplication and division in time domain yield addition and subtraction in frequency domain. I also noticed that convolution in time domain results in multiplication in frequency domain so line 4 of the table looks wrong also...
Can someone clear this up or maybe provide a better summary of the different operations in time domain and how they translate in frequency domain?
Somewhat-related question: link.