Let c = (c0, c1,... , cn-1)T Cn be the vector of discrete Fourier coefficients corresponding to the sample vector f = (f0, f1,..., fn-1)T.

Let c = (c0, c1,... , cn-1)T ˆŠ Cn be the vector of discrete Fourier coefficients corresponding to the sample vector f = (f0, f1,..., fn-1)T.
(a) Explain why the sampled signal f = Fn c can be reconstructed by multiplying its Fourier coefficient vector by an n × n matrix Fn. Write down F2, F3, F4, and F8. What is the general formula for the entries of Fn?
(b) Prove that, in general,

where €  denotes the Hermitian transpose defined in Exercise 5.3.25.
(c) Prove that

is a unitary matrix, i.e., U1n = U-n.

F