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For the signal given below, check whether it is a power signal or an energy signal or neither. X(t) 2 -1 0 2e-¹/2

For the signal given below, check whether it is a power signal or an energy signal or neither. X(t) 2 -1 0 2e-¹/2

Introductory Circuit Analysis (13th Edition)
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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**Educational Topic: Signal Analysis** **Title: Signal Classification: Power Signal vs. Energy Signal** **Content:** In this educational segment, we will analyze the given signal to determine whether it is a power signal, an energy signal, or neither. **Signal Description:** The plotted signal, \(X(t)\), is defined on the time-axis \(t\). It consists of two parts: 1. A rectangular pulse of height 2, spanning from \(t = -1\) to \(t = 0\). 2. An exponentially decaying curve defined by \(2e^{-t/2}\) for \(t \geq 0\). **Diagram Explanation:** - The rectangular pulse is displayed as a vertical bar from \(-1\) to \(0\) on the \(t\)-axis, with a constant amplitude of 2. - Starting from \(t = 0\), the exponential curve begins, decreasing towards zero as \(t\) increases. It demonstrates an exponential decay characteristic determined by the function \(2e^{-t/2}\). **Task at Hand:** To classify the signal, follow these steps: 1. **Energy Signal Check:** Evaluate the total energy \(E = \int_{-\infty}^{\infty} |X(t)|^2 \, dt\). If this integral is finite and non-zero, the signal is an energy signal. 2. **Power Signal Check:** Calculate the average power \(P = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} |X(t)|^2 \, dt\). If this evaluates to a finite positive value, the signal is a power signal. 3. **Neither:** If neither the energy nor the power criteria are satisfied, the signal is classified as neither. In the next section, we will demonstrate the mathematical evaluation of these criteria using the given signal.
Transcribed Image Text:**Educational Topic: Signal Analysis** **Title: Signal Classification: Power Signal vs. Energy Signal** **Content:** In this educational segment, we will analyze the given signal to determine whether it is a power signal, an energy signal, or neither. **Signal Description:** The plotted signal, \(X(t)\), is defined on the time-axis \(t\). It consists of two parts: 1. A rectangular pulse of height 2, spanning from \(t = -1\) to \(t = 0\). 2. An exponentially decaying curve defined by \(2e^{-t/2}\) for \(t \geq 0\). **Diagram Explanation:** - The rectangular pulse is displayed as a vertical bar from \(-1\) to \(0\) on the \(t\)-axis, with a constant amplitude of 2. - Starting from \(t = 0\), the exponential curve begins, decreasing towards zero as \(t\) increases. It demonstrates an exponential decay characteristic determined by the function \(2e^{-t/2}\). **Task at Hand:** To classify the signal, follow these steps: 1. **Energy Signal Check:** Evaluate the total energy \(E = \int_{-\infty}^{\infty} |X(t)|^2 \, dt\). If this integral is finite and non-zero, the signal is an energy signal. 2. **Power Signal Check:** Calculate the average power \(P = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} |X(t)|^2 \, dt\). If this evaluates to a finite positive value, the signal is a power signal. 3. **Neither:** If neither the energy nor the power criteria are satisfied, the signal is classified as neither. In the next section, we will demonstrate the mathematical evaluation of these criteria using the given signal.
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