True or False ### Required InformationConsider the following signals.\[ g(t) = 4 \left( \delta_4 (t + 1) - \delta_4 (t - 3) \right) \]The CTFT of \( g(t) \) is 0.#### Explanation:1. **Notation**: - \(\delta_4(t + 1)\) and \(\delta_4(t - 3)\) likely refer to delayed or shifted impulse functions. The subscript 4 could denote a specific characteristic of these impulses, such as their scaling or a system they are part of.2. **Formula**: - The given formula combines two impulse functions, with \(\delta_4(t + 1)\) shifted to the left by 1 unit, and \(\delta_4(t - 3)\) shifted to the right by 3 units. The difference is then scaled by a factor of 4.3. **CTFT Result**: - The Continuous-Time Fourier Transform (CTFT) of \( g(t) \) is stated to be 0, indicating that this specific combination of impulses results in a signal with no frequency components.

Answered: 8 (t) = 4(84 (t + 1) – 84 (t – 3)) |…

Engineering

Electrical Engineering

8 (t) = 4(84 (t + 1) – 84 (t – 3)) | The CTFT of g(f) is O.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Concept explainers

Fault Analysis

In an electrical engineering system, a fault is an abnormal electric current flowing through the system, and fault analysis is the study of these faults. For instance, a short-circuit is a fault where the live wire touches the ground or neutral wire. If a circuit is interrupted by a failure of a current-carrying wire then an open circuit fault occurs. The open-circuit faults are also called series faults. One or more phases or ground may be involved in a three-phase fault or may occur only between two phases. Current flows into the earth in case of a ground fault or earth fault. For most situations, the prospective short circuit current of a fault that is predictable can be calculated. To limit the loss of service because of a failure, the protective devices can detect fault conditions and operate circuit breakers and also other devices. All phases equally can be affected in a poly-phase system which is known as symmetric electrical fault. The asymmetric fault becomes more complicated to analyze if only some phases are affected. By using methods such as symmetrical components, the power system analysis of these types of faults is often simplified. The main objective of power system protection is to design, detect, and interrupt power system faults.

Question

True or False

### Required Information

Consider the following signals.

\[ g(t) = 4 \left( \delta_4 (t + 1) - \delta_4 (t - 3) \right) \]

The CTFT of \( g(t) \) is 0.

#### Explanation:

1. **Notation**:
- \(\delta_4(t + 1)\) and \(\delta_4(t - 3)\) likely refer to delayed or shifted impulse functions. The subscript 4 could denote a specific characteristic of these impulses, such as their scaling or a system they are part of.

2. **Formula**:
- The given formula combines two impulse functions, with \(\delta_4(t + 1)\) shifted to the left by 1 unit, and \(\delta_4(t - 3)\) shifted to the right by 3 units. The difference is then scaled by a factor of 4.

3. **CTFT Result**:
- The Continuous-Time Fourier Transform (CTFT) of \( g(t) \) is stated to be 0, indicating that this specific combination of impulses results in a signal with no frequency components.

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