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Consider an LTI non-recursive DT system given as:

y[n]=x[n]−5⋅x[n−2]+3⋅x[n−3]−x[n−5]
find the impulse response (unit sample response) of this system, h[n].

User Minudika
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Final answer:

The impulse response of the given LTI non-recursive DT system, h[n], is found by inputting an impulse function into the system. The impulse response yields specific values at n = 0, 2, 3, and 5, and is zero at all other times.

Step-by-step explanation:

The student's question involves finding the impulse response, h[n], of a linear time-invariant (LTI) non-recursive discrete-time (DT) system. The system is described by its input-output relationship: y[n] = x[n] - 5 ⋅ x[n-2] + 3 ⋅ x[n-3] - x[n-5]. To find the impulse response, we consider the response of the system when the input x[n] is an impulse function, δ[n], which is 1 at n = 0 and 0 at all other times.

The impulse response h[n] will be the output of the system y[n] when x[n] = δ[n]. Substituting the impulse function into the equation, we obtain: h[n] = δ[n] - 5⋅δ[n-2] + 3⋅δ[n-3] - δ[n-5]. Therefore, h[n] will be 1 at n = 0, -5 at n = 2, 3 at n = 3, and -1 at n = 5, and will be 0 for all other values of n.

User Kittycat
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