Let c = (c0, c1,... , cn-1)T Cn be the vector of discrete Fourier coefficients corresponding to
Question:
(a) Explain why the sampled signal f = Fn c can be reconstructed by multiplying its Fourier coefficient vector by an n à 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.
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a In view of 213 formula 591 is equivalent to matrix multiplication f F n c where is th...View the full answer
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