Question
Download Solution PDFIf a discrete signal represented by x[n] = αn u(n), then what is the value of the signal g(n) = x(n) - αx(n - 1)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
The graph of x[n] = αn u(n),
(α > 0)
⇒ it starts from n=0.
The graph of αx(n - 1),
⇒ it starts from n = 1.
g(n) is obtained by subtraction of both graphs.
Hence,
g(n) = δ(n).
Alternate Method
g(n) = x(n) - αx(n - 1) where (α > 0)
⇒ g(n) = αn u(n) - α*αn-1 u(n-1)
⇒ g(n) = αn u(n) - αn u(n-1)
⇒ g(n) = δ(n).
Last updated on Jul 2, 2025
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