Question

The discrete system \( y[n] = x[n-3] - 4x[n-7] \) is a _______.

• A. Dynamic system
• B. Time varying system
• C. Memory-less system
• D. Non-linear system

Hint:

If output depends on delayed input → it's dynamic. Memory-less = only \( x[n] \).

Answer 1

The Correct Option is A

Step 1: Definition of Dynamic System
A system is dynamic if the output depends on past or future input values. Step 2: Analyze the Given System
Here, the output \( y[n] \) depends on:
- \( x[n - 3] \): a past input
- \( x[n - 7] \): a further past input
This clearly indicates memory and hence, it's a dynamic system.
Step 3: Eliminate Wrong Options
- Memory-less → would only depend on \( x[n] \)
- Time-varying → time index coefficients must vary
- Non-linear → no nonlinear operation here
Conclusion:
Option (1) is correct — it is a dynamic system.