An LTI system has the relationship y[n] = โˆ‘ ๐‘ฅ[๐‘˜]๐‘”[๐‘› โˆ’ 2๐‘˜]โˆž๐‘˜= โˆ’โˆž , where g[n] = u[n] โ€“u[n-4]. Determine y[n] if a) x[n] = ฮด[n-1], b) x[n] = ฮด[n-2].

Question

An LTI system has the relationship y[n] = โˆ‘ ๐‘ฅ[๐‘˜]๐‘”[๐‘› โˆ’ 2๐‘˜]โˆž๐‘˜= โˆ’โˆž , where g[n] = u[n] โ€“u[n-4]. Determine y[n] if a) x[n] = ฮด[n-1], b) x[n] = ฮด[n-2].
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Solution 1

To determine y[n] for the given LTI system, we need to substitute the given values of x[n] into the equation y[n] = โˆ‘ ๐‘ฅ[๐‘˜]๐‘”[๐‘› โˆ’ 2๐‘˜]โˆž๐‘˜= โˆ’โˆž and simplify the expression.

a) For x[n] = ฮด[n-1], we substitute this value into the equation:

y[n] = โˆ‘ ฮด[k-1] * g[n - 2k] from k = -โˆž to โˆž

Since ฮด[k-1] is non Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve stud

is non Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you t

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