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Consider a discrete-time system with input x[n] and output y[n]. The input-output relationship for this system is y[n]=x[n]x[n−2]. (a) Is the system memoryless?
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Consider a discrete-time system with input x[n] and output y[n]. The input-output relationship for this system is y[n]=x[n]x[n−2]. (a) Is the system memoryless?

User ExiRe
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Final answer:

The discrete-time system described is not memoryless.

Step-by-step explanation:

Memoryless systems are those where the output at a given time depends only on the input at that same time and does not depend on any past inputs or outputs.

In this case, the output y[n] is determined by the current input x[n] and the input two steps earlier, x[n-2]. Since the output relies on past inputs, the system is not memoryless.

For example, if x[0] = 3 and x[-2] = 2, then y[0] = x[0] * x[0-2] = 3 * 2 = 6.

User Tawn
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