**Response of an LTI Discrete Time System to a Unit Step Input**

When we have an LTI (Linear Time-Invariant) discrete-time system, the response to a unit step input u(n) is given by the impulse response of the system, which is commonly denoted as h(n).

In this case, the given impulse response is delta(n), which represents an impulse at n = 0. The unit step function u(n) is defined as:

u(n) = 0, for n < />
u(n) = 1, for n >= 0

To find the response of the system to the input nu(n), we need to convolve the input signal with the impulse response.

**Convolution of nu(n) and delta(n):**

The input signal nu(n) can be expressed as the product of n and u(n):

nu(n) = n * u(n)

The impulse response delta(n) is non-zero only at n = 0, and it has the value 1 at that point.

Therefore, the convolution of nu(n) and delta(n) can be written as:

(nu * delta)(n) = sum over k of [nu(k) * delta(n-k)]

Since delta(n-k) is non-zero only when n = k, the sum collapses to a single term:

(nu * delta)(n) = nu(n) * delta(0)

**Simplifying the Convolution:**

Now, let's simplify the convolution further. We know that delta(0) = 1, so:

(nu * delta)(n) = nu(n) * 1

Therefore, the response of the system to the input nu(n) is:

(nu * delta)(n) = nu(n)

**Interpretation:**

The response of the system to the input nu(n) is given by u(n-1). This means that the output of the system will be a delayed version of the unit step function by one sample.

In other words, at n = 0, the output will be 0. From n = 1 onwards, the output will be 1, indicating a step response. This delay of one sample arises from the convolution operation, where the impulse response is located at n = 0.

Therefore, the correct answer is u(n-1).