If x(n) is a discrete-time signal, then the value of x(n) at non-integer value of ’n’ is

Understanding the Problem

The question requires us to find the value of a discrete-time signal $x(n)$ at a non-integer value of $n$.

Relevant Concepts

1. Discrete-Time Signal: A signal defined only at discrete intervals, typically represented by integer values of $n$.
2. Sampling: In discrete-time systems, there is no defined value of the signal at non-integer points unless interpolation is applied.

Analysis and Detail

Discrete-time signals are defined only at integer values of $n$ (e.g., $n = 0, 1, 2, \ldots$). As such, there is no inherent value for $x(n)$ when $n$ is non-integer (e.g., $n = 1.5$).

To estimate the value of $x(n)$ at non-integer points, interpolation techniques may be used, such as:

• Linear Interpolation: Estimating $x(n)$ by taking a weighted average of neighboring integer values $x(n-1)$ and $x(n)$.
• Spline or Polynomial Interpolation: More complex methods that provide smoother approximations.

Verify and Summarize

Since $x(n)$ is not defined for non-integer $n$, it cannot be evaluated directly without using interpolation techniques. The choice of interpolation method would depend on the desired accuracy and the characteristics of the signal.

Final Answer

The value of $x(n)$ at non-integer values of $n$ cannot be determined directly from the discrete-time signal definition and requires interpolation methods to estimate it.