(New page: ==Part a== The system is NOT time-invariant The general formulas for te system are: x[n] = d[n-k] y[n] = (k+1)^2 * d[n-(k+1)] Shifting by a constant means that x[n-a] = d[n-k-a] y[n...)
 
(Part b)
 
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==Part b==
 
==Part b==
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The input X[n] = u[n] will yield y[n] = u[n-1] because the system is linear.

Latest revision as of 16:59, 11 September 2008

Part a

The system is NOT time-invariant

The general formulas for te system are:

x[n] = d[n-k]

y[n] = (k+1)^2 * d[n-(k+1)]

Shifting by a constant means that

x[n-a] = d[n-k-a]

y[n-a] = (k+1)^2 * d[n-(k+1)-a]

As seen from this procedure, when shifted the y[n-a] has a multiplying (k+1)^2 that does not yield the same value as in the nonshifted equation.

Part b

The input X[n] = u[n] will yield y[n] = u[n-1] because the system is linear.

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett