If x(n) = [1,2,0,3, -2,4,7,5] evaluate the following i) X (0) ii) X (4) iii) ∑ 𝑋(𝐾) 7 𝑘=0 iv) ∑ |𝑋(𝐾)| 7 𝑘=0 2

Question

If x(n) = [1,2,0,3, -2,4,7,5] evaluate the following

i) X (0)
ii) X (4)
iii) $\sum_{k=0}^{7} X(K)$
iv) $\sum_{k=0}^{7} |X(K)|$

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Solution

i) X(0) refers to the first element in the sequence x(n). In this case, X(0) = 1.

ii) X(4) refers to the fifth element in the sequence x(n). In this case, X(4) = -2.

iii) ∑ 𝑋(𝐾) 7 𝑘=0 refers to the sum of all elements in the sequence from the first element (k=0) to the eighth element (k=7). In this case, ∑ 𝑋(𝐾) 7 𝑘=0 = 1 + 2 + 0 + 3 - 2 + 4 + 7 + 5 = 20.

iv) ∑ |𝑋(𝐾)| 7 𝑘=0 2 refers to the sum of the absolute values of all elements in the sequence from the first element (k=0) to the eighth element (k=7). The 2 at the end seems to be a typo as it doesn't fit into the notation. Assuming it's a typo, ∑ |𝑋(𝐾)| 7 𝑘=0 = |1| + |2| + |0| + |3| + |-2| + |4| + |7| + |5| = 24.

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If x(n) = [1,2,0,3, -2,4,7,5] evaluate the following i) X (0) ii) X (4) iii) ∑ 𝑋(𝐾) 7 𝑘=0 iv) ∑ |𝑋(𝐾)| 7 𝑘=0 2

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