Q2. Find the Fourier Series in Trigonometric format (sine/cosine format). f(t) = 1. -1, T 2 osts and it has a period of T. -15150
Q2. Find the Fourier Series in Trigonometric format (sine/cosine format). f(t) = 1. -1, T 2 osts and it has a period of T. -15150
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Problem 2: Fourier Series in Trigonometric Format
**Objective:**
Find the Fourier Series in trigonometric format (sine/cosine format) for the function given below, which has a period of \(T\).
**Function Definition:**
\[
f(t) =
\begin{cases}
1, & 0 \leq t \leq \frac{T}{2} \\
-1, & -\frac{T}{2} \leq t < 0
\end{cases}
\]
The problem requires expressing the periodic function \(f(t)\) using Fourier series composed of sine and cosine terms. The function is piecewise defined over the interval \([-T/2, T/2]\) and has a periodicity of \(T\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2828890-e758-4d3f-889f-4bdd3ee1fb27%2F67183b78-ac90-44b9-9840-2063a2c849b7%2Fpiffn7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 2: Fourier Series in Trigonometric Format
**Objective:**
Find the Fourier Series in trigonometric format (sine/cosine format) for the function given below, which has a period of \(T\).
**Function Definition:**
\[
f(t) =
\begin{cases}
1, & 0 \leq t \leq \frac{T}{2} \\
-1, & -\frac{T}{2} \leq t < 0
\end{cases}
\]
The problem requires expressing the periodic function \(f(t)\) using Fourier series composed of sine and cosine terms. The function is piecewise defined over the interval \([-T/2, T/2]\) and has a periodicity of \(T\).
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