MATH 104AHomework 5General Instructions:You have to integrate all the problems that require coding and/ornumerical computation in a singlejupyternotebook. Make sure all your codes have a preamblewhich describes purpose of the code, all the input variables, the expected output, your name,and the date of the last time you modified it. Write your own code, individually. Do not copycodes! The solutions to the problems that do not require coding must be uploaded as a singlepdf or as part of thejupyternotebook.The Discrete Fourier Transform (DFT) of a periodic arrayfj,forj= 0,1, . . . , N-1 (cor-responding to data at equally spaced points, starting at the left end point of the interval ofperiodicity) is evaluated via the Fast Fourier Transform (FFT) algorithm (Npower of 2). Usean FFT package, i.e. an already coded FFT (e.g. scipy.↵tpack or numpy.↵t).