2. For any frequency o consider the (complex-valued) function Wa(t) = e-2mot. We can use this function to make vectors in C" by sampling in the
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How do I approach parts a, b & c? I don't understand this question. Thanks in advance.

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NTH 710 - Q2.png

NTH 710 - Q2.png

2. For any frequency o consider the (complex-valued) function Wa(t) = e-2mot. We can use this function
to make vectors in C" by sampling in the time domain. For j = 0, 1, ... n - 1 let t; = ~. Define a
vector, Wa = (w[0], w[1], ..., win - 1]) by the formula w[j] = wa(t;).
n
(a) For a given value of o calculate | |Wall.
(b) Show that the collection of vectors { Wo, W1, . .., Wn-1} is orthogonal. Is it also orthonormal?
(c) Consider the n x n matrix (with complex values) W whose entries are given by Wik =
e-2nijk/n
Vn
This is the matrix whose kth column is w /Vn. Show that W is a unitary matrix.

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