*please do in python*

Write a computer program that calculates the discrete Fourier transform (and inverse transform) for a set of sampled data of arbitrary length N with arbitrary interval spacing A Apply your code to the following problems: a) Testing your code with analytic input Consider the following analytic functions: y,(1)-sin(2TI)-2 sinod.1)-3 sin(10TI) ,(1)-5 sin (24,1) + 2 cos(6TU) + sin(10.,) Sample these functions and apply the DFT code you wrote to obtain the Fourier transfoms Y ) for i =1 to 3, Create samples that are both under sampled and sufficiently sampled, and test the effect of changing the interval spacing and the total time interval. Discuss your results. Do the values of the FT you obtained for the sufficiently sampled case corespond with what you would expect? Also, discuss the expected symmetry of your DFT based on the symmetry of the analytic functions above Try the case where the functions above are and are not periodic in the time sampling window What happens? Why, and what can be done to improve your spectrum? Finally, apply your code to obtain the inverse Fourier transforms of the Y(f). Discuss your results