8 (t) = 4(84 (t + 1) – 84 (t – 3)) | The CTFT of g(f) is O.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b94d5d1-8249-4b1b-8d70-6007d482e8f0%2F80a036e8-81fa-49d8-8f74-785e93d3c01e%2Fuhki9ny_processed.png&w=3840&q=75)
Transcribed Image Text:### 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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