Question
Download Solution PDFWhat is the convolution y[n] = x[n]*h[n] : where x[n] = an u[n], h[n] = βn u[n], α ≠ β, α = 0.8, β = 0.9 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
y(n) = x(n) * h(n)
⇃↾ ⇃↾ z transform
Y(z) = X(z) . H(z)
Calculation:
x(n) ↔ x(z)
an u[n] ↔
h[n] ↔ H(z)
βn u[n] ↔
Y(z) = X(z).H(z)
Y(z) =
⇒ Doing partial fractions and replacing value of α and β we get:
Y(x) =
⇒ Doing inverse z-transform we get
y(n) = -8(0.8)n u(n) + 9(0.9)n u(n)
Last updated on Jul 2, 2025
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