Find Z transform of the given function x(n). Need very urgent help. ### Mathematical Expression on Discrete SignalsThe equation provided represents a discrete-time signal \( x[n] \):\[ x[n] = -0.5 \delta[n + 1] + \delta[n] \]#### Explanation:- **\( x[n] \)**: Represents the discrete signal at time index \( n \).- **\( \delta[n] \)**: The Kronecker delta function, a discrete analog of the Dirac delta function. It is defined as: \[ \delta[n] = \begin{cases} 1 & \text{if } n = 0 \\ 0 & \text{otherwise} \end{cases} \] This function is used to denote impulse signals in discrete time.- **\( \delta[n + 1] \)**: Represents a shifted delta function. The shift \( +1 \) indicates a delay by one sample in the positive direction of the index \( n \).- **Coefficients**: - **\(-0.5\)**: This is a scaling factor applied to the \( \delta[n + 1] \) term, indicating that the impulse at \( n = -1 \) will be scaled down by half.#### Signal Description:This equation describes a signal that consists of two impulses:- An impulse at \( n = 0 \) with a magnitude of 1.- A scaled impulse at \( n = -1 \) with a magnitude of \(-0.5\).This signal can be visualized as discrete spikes occurring at the specified indices.

The expression of the discrete-time function is given as xn=-0.5δn+1+δn--->(1)

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Find Z transform of the given function x(n)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

Find Z transform of the given function x(n). Need very urgent help.

### Mathematical Expression on Discrete Signals

The equation provided represents a discrete-time signal \( x[n] \):

\[ x[n] = -0.5 \delta[n + 1] + \delta[n] \]

#### Explanation:

- **\( x[n] \)**: Represents the discrete signal at time index \( n \).

- **\( \delta[n] \)**: The Kronecker delta function, a discrete analog of the Dirac delta function. It is defined as:
\[
\delta[n] =
\begin{cases}
1 & \text{if } n = 0 \\
0 & \text{otherwise}
\end{cases}
\]
This function is used to denote impulse signals in discrete time.

- **\( \delta[n + 1] \)**: Represents a shifted delta function. The shift \( +1 \) indicates a delay by one sample in the positive direction of the index \( n \).

- **Coefficients**:
- **\(-0.5\)**: This is a scaling factor applied to the \( \delta[n + 1] \) term, indicating that the impulse at \( n = -1 \) will be scaled down by half.

#### Signal Description:
This equation describes a signal that consists of two impulses:
- An impulse at \( n = 0 \) with a magnitude of 1.
- A scaled impulse at \( n = -1 \) with a magnitude of \(-0.5\).

This signal can be visualized as discrete spikes occurring at the specified indices.

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