Let fnon = 0,.... N - 1, be real data with N = 2m. Let Fy, k = 0,..., N -1, be the discrete Fourier transform of the data. Suppose the f, values satisfy the symmetry property In = fN-n (n=1,.., N-1). (a) [7 marks] By manipulating indices, express the Fourier coefficients F, in terms of only the first N/2 + 1 independent data values. (b) [7 marks] Show that Fourier coefficients Fx are all purely real numbers. Hint: if z is a complex number then z + z is real