Question about Fourier Series/Transform

[Joseph Yellow]

Hi guys, I'm now studying Fourier series/transform for representing signals in the frequency domain.

I'm having a bit of a hard time getting the gist of it. Right now I'm using the book "signals and systems" (oppenheim) because that's the one my teacher uses.

My problem is this: both the book and my teacher divide the subject into a lot of segments:

• Fourier series for discrete time periodic signals.
  
  
• Fourier series for continuous-time periodic signals.
  
  
• Fourier transform for discrete-time aperiodic signals.
  
  
• Inverse Fourier transform for discrete-time aperiodic signals.
  
  
• Fourier transform for continuous-time aperiodic signals.
  
  
• Inverse Fourier transform for continuous-time aperiodic signals.
  
  
• Fourier transform for discrete-time periodic signals.
  
  
• Inverse Fourier transform for discrete-time periodic signals.
  
  
• Fourier transform for continuous-time periodic signals.
  
  
• Inverse Fourier transform for continuous-time periodic signals.

Although the formulas are pretty similar, the method for each one differs a little bit (as far as I understood it at least), and I'm getting a little bit overwhelmed as I'm trying to get it all.

My question is if need to remember every single little detail about each case or if there's something I'm not getting and there is a more intuitive/general way to think and solve problems involving any of the cases listed above.

If anyone has a good alternative resource (video/text) to Oppenheim's book I would be very glad to hear about it too.

Thanks in advance.

 

[FactChecker]

As you suspect, they can all be done in a fairly unified way. But doing that may require studying concepts (generalized functions, test functions, etc.) that may take some patience and some more mathematical theory. There is an excellent Stanford lecture series on youtube that presents a unified theory
(see ).
It consists of 30 lectures, but you may satisfy your intellectual curiosity with fewer. I found all 30 to be worth while.

 

[scottdave]

...There is an excellent Stanford lecture series on youtube that presents a unified theory
(see ).

This video lecture looks interesting. I will check it out.