@dharr Thank you once again. 

@Rouben Rostamian  Yes. I did notice that briefly. I deliberately wanted to do things from ground up so that I can learn Maple and Fourier transforms.

@dharr I notice that the when I use the animate plot option, the sheet that you have provided works perfeclty. But when i use the same command it says that "add" in fourier_f needs numeric inputs. Interesingly, when I explicitly give fourier_f a numeric argument it gives the plot. The animate option doesn't work though. Everything works fine in your sheet even though the commands are exactly the same. Perhaps a version issue ?

@dharr 

I see. So the "sum" generates a general formula. That's what it was printing out over multiple lines with different operators. Thank you for pointing out what was slowing down the sheet. That posint assumption was very helpful.

Thanks a lot for the delay operator explanation.

Overall, it was really helpful. 

@dharr Thank you. I just now found out that there is a difference between " . " and " * ". I changed that. 

I wanted to animate the fourier sum as a function of N usinf the "animate" option. In general, I wanted a simplified form of the coefficients and the Foruier representation so that I can check the result with textook examples. Overall, I am trying to build a worksheet which can help me in understanding different properties of Fourier transform given a target function. 

I checked the "sum" function. It's form seems closes to the textbook style and it also computes the equation rather than finite values. 

I have uploaded the sheet. In the end  of the sheet I am trying to display the target function and it's Fourier representation.

fourier_analysis.mw

EDIT - Why have you used add as 'add' in commas? What's the reason for this ?