The impulse response of a system is given by h[n] = 2^n u[n+2]. To determine whether the system is causal, stable, or neither, we need to understand the definitions of these terms: 1. A system is causal if the output at any time depends only on the values of the input at the present and past times. It does not depend on future values of the input. 2. A system is stable if, when the input is bounded, the output is also bounded. Now, let's analyze the given system: The system is defined by h[n] = 2^n u[n+2]. The unit step function u[n+2] shifts the function 2^n to the left by two units. This means that for n = -2, h[n] = 2^n. 1. Causality: Since the output at time n depends on the value of the input at time n+2 (which is a future time), the system is not causal. 2. Stability: The function 2^n grows exponentially for positive n, which means that the output can become unbounded for a bounded input. Therefore, the system is not stable. So, the system is non-causal and not stable.

Question

The impulse response of a system is given by h[n] = 2^n u[n+2]. To determine whether the system is causal, stable, or neither, we need to understand the definitions of these terms:

1. A system is causal if the output at any time depends only on the values of the input at the present and past times. It does not depend on future values of the input.

2. A system is stable if, when the input is bounded, the output is also bounded.

Now, let's analyze the given system:

The system is defined by h[n] = 2^n u[n+2]. The unit step function u[n+2] shifts the function 2^n to the left by two units. This means that for n < -2, h[n] = 0, and for n >= -2, h[n] = 2^n.

1. Causality: Since the output at time n depends on the value of the input at time n+2 (which is a future time), the system is not causal.

2. Stability: The function 2^n grows exponentially for positive n, which means that the output can become unbounded for a bounded input. Therefore, the system is not stable.

So, the system is non-causal and not stable.

Knowee AI · Accepted Answer

The impulse response of a system is given by h[n] = 2^n u[n+2]. To determine whether the system is causal, stable, or neither, we need to understand the definitions of these terms:

1. A system is causal if the output at any time depends only on the values of the input at the present and past times. It does not depend on future values of the input.

2. A system is stable if, when the input is bounded, the output is also bounded.

Now, let's analyze the given system:

The system is defined by h[n] = 2^n u[n+2]. The unit step function u[n+2] shifts the function 2^n to the left by two units. This means that for n < -2, h[n] = 0, and for n >= -2, h[n] = 2^n.

1. Causality: Since the output at time n depends on the value of the input at time n+2 (which is a future time), the system is not causal.

2. Stability: The function 2^n grows exponentially for positive n, which means that the output can become unbounded for a bounded input. Therefore, the system is not stable.

So, the system is non-causal and not stable.

Impulse response of a system is given by h[n] = 2^n u[n+2]. The system is 1 pointCausal but not stableStable and causalStable but not causalnon-causal and not stable

Question

Solution

Similar Questions

Upgrade your grade with Knowee