2 Determine the Fourier series representation of the function f(t) defined by 3 T(1) = {₁ f(t+4)-f(t). -5 -2<1<0 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem: Fourier Series Representation**

Determine the Fourier series representation of the function \( f(t) \) defined by:

\[
f(t) = 
\begin{cases} 
3, & \text{for } -2 < t < 0 \\
-5, & \text{for } 0 < t < 2 
\end{cases}
\]

The function satisfies the periodic condition: \( f(t+4) = f(t) \).

This problem involves finding the Fourier series for the given piecewise function \( f(t) \), which is periodic with a period of 4. The function takes different constant values over the intervals \((-2, 0)\) and \((0, 2)\).
Transcribed Image Text:**Problem: Fourier Series Representation** Determine the Fourier series representation of the function \( f(t) \) defined by: \[ f(t) = \begin{cases} 3, & \text{for } -2 < t < 0 \\ -5, & \text{for } 0 < t < 2 \end{cases} \] The function satisfies the periodic condition: \( f(t+4) = f(t) \). This problem involves finding the Fourier series for the given piecewise function \( f(t) \), which is periodic with a period of 4. The function takes different constant values over the intervals \((-2, 0)\) and \((0, 2)\).
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