USING PYTHON

a) a code to compute a spectral approximation to the derivative using one DFT and one inverse DFT b) test your code c) observe the behavior of the error as N is increased to 16 and 32.

Note that PM ( ) is again a trigonometric polynomial of degree s N / 2 and whose coefficients can be computed from those of PN ( ) via the FFT. ( 2 ) Write a code to compute a ( spectral ) approximation to the derivative at in , = ( 27 / N ) for j 1 1 . N - 1 for the corresponding periodic array j j = 0 , I N - 1 using one DET and one inverse DET le . in order Nozz N operations . ( b ) Test your code by comparing with your answer of the previous problem . ( 6 ) Observe the I ehavior of the error as N is increased to 16 and 32 Note the contribution to the derivative from the K - N / 2 node should be zero . Make sure to set the Fourier coefficient for k - N / 2 of the derivative equal to zero