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To determine the Fourier series of the given signal in Gambar B3, we first need to analyze the periodicity and the nature of the signal. 

The signal \( x(t) \) depicted in Gambar B3 appears to be a periodic rectangular wave with a period \( T \). We need to express this signal in terms of its Fourier series representation:

\[ x(t) = \sum_{n=-\infty}^{\infty} c_n e^{j n \omega_0 t} \]

where \( \omega_0 = \frac{2\pi}{T} \) is the fundamental angular frequency, and \( c_n \) are the Fourier coefficients given by:

\[ c_n = \frac{1}{T} \int_{0}^{T} x(t) e^{-j n \omega_0 t} \, dt \]

### Step-by-Step Solution:

1. **Determine the period \( T \)**:
   From the figure, it appears that the signal has a period of \( T = 6 \) units (from \( t = 0 \) to \( t = 6 \)).

2. **Express the signal mathematically**:
   The signal \( x(t) \) can be described as a piecewise function over one period \( T \):

   \[
   x(t) = \begin{cases} 
   3 & 1 \leq t < 3 \\
   -1 & 3 \leq t < 4 \\
   0 & \text{otherwise in the period}
   \end{cases}
   \]

3. **Compute the Fourier coefficients \( c_n \)**:
   Using the definition of \( c_n \):

   \[
   c_n = \frac{1}{6} \left[ \int_{1}^{3} 3 e^{-j n \omega_0 t} \, dt + \int_{3}^{4} (-1) e^{-j n \omega_0 t} \, dt \right]
   \]

   With \( \omega_0 = \frac{2\pi}{6} = \frac{\pi}{3} \).

   - For the first interval \( 1 \leq t < 3 \):

     \[
     \int_{1}^{3} 3 e^{-j n \frac{\pi}{3} t} \, dt = 3 \int_{1}^{3} e^{-j n \frac{\pi}{3} t} \, dt = \frac{3}{-j n \frac{\pi}{3}} \left[ e^{-j n \frac{\pi}{3} t} \right]_{1}^{3} = \frac{9}{-j n \pi} \left( e^{-j n \pi} - e^{-j n \frac{\pi}{3}} \right)
     \]

   - For the second interval \( 3 \leq t < 4 \):

     \[
     \int_{3}^{4} (-1) e^{-j n \frac{\pi}{3} t} \, dt = -\int_{3}^{4} e^{-j n \frac{\pi}{3} t} \, dt = \frac{-1}{-j n \frac{\pi}{3}} \left[ e^{-j n \frac{\pi}{3} t} \right]_{3}^{4} = \frac{3}{j n \pi} \left( e^{-j n \frac{4\pi}{3}} - e^{-j n \pi} \right)
     \]

   Combining these results:

   \[
   c_n = \frac{1}{6} \left( \frac{9}{-j n \pi} \left( e^{-j n \pi} - e^{-j n \frac{\pi}{3}} \right) + \frac{3}{j n \pi} \left( e^{-j n \frac{4\pi}{3}} - e^{-j n \pi} \right) \right)
   \]

   Simplifying this will give the final expression for \( c_n \).

### Summary:
The Fourier series coefficients \( c_n \) can be computed using the above integrals and simplifications. The signal \( x(t) \) is then expressed as the sum of these coefficients multiplied by the exponential functions. The exact coefficients will depend on further simplification and evaluation of the exponential terms.

Would you like a more detailed simplification of these coefficients, or do you have any specific questions regarding the Fourier series?

### Suggested Questions:
1. Can you provide the complete simplified form of the Fourier coefficients \( c_n \)?
2. How do you determine the amplitude spectrum of the signal?
3. What is the significance of the fundamental frequency \( \omega_0 \) in this context?
4. How does the periodicity of the signal affect its Fourier series representation?
5. Can you explain the physical interpretation of the Fourier series for this signal?

### Tip:
When dealing with Fourier series, always ensure to correctly identify the period and piecewise nature of the signal, as these are critical in calculating the Fourier coefficients accurately.

Learn how to compute the Fourier series of a periodic rectangular wave signal depicted in Gambar B3. Detailed step-by-step solution including Fourier coefficients calculation and signal periodicity analysis.

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