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The text describes a problem involving Frequency Shift Keying (FSK) modulation for a digital signal. Let's break down the requirements and calculate the answers based on the information provided:

### Given:
- **Modulation type**: FSK with 2 states.
- **Modulated signal bandwidth**: \( 720 \, \text{MHz} \).
- **Modulation index**: \( h = 8 \).
- **Carrier signal**: \( S(t) = 12 \cos(25.133 \times 10^9 t + 20) \), where \( 25.133 \times 10^9 \) represents the carrier frequency.

We are tasked with calculating the following:

1. **Adjacent Frequencies (f1 and f2)**:
   - The formula for calculating the frequencies in FSK modulation is:
     \[
     f_1 = f_c - \Delta f
     \]
     \[
     f_2 = f_c + \Delta f
     \]
     where \( \Delta f \) is the frequency deviation.

     The modulation index \( h \) is related to the frequency deviation \( \Delta f \) by:
     \[
     h = \frac{2 \Delta f}{R_b}
     \]
     where \( R_b \) is the bit rate, which is related to the bandwidth.

2. **Percentage Frequency Deviation**:
   - Calculate the percentage deviation using the formula:
     \[
     \text{Percentage Deviation} = \frac{\Delta f}{f_c} \times 100
     \]

3. **Transmission Speed**:
   - The transmission speed \( V_t \) is related to the bit rate \( R_b \).

Let me calculate these values based on the provided details.### Calculated Results:
1. **Adjacent Frequencies**:
   - \( f_1 = 24.813 \, \text{GHz} \)
   - \( f_2 = 25.453 \, \text{GHz} \)

2. **Percentage Frequency Deviation**:
   - \( 1.27\% \)

3. **Transmission Speed (bit rate)**:
   - The bit rate \( R_b = 720 \, \text{MHz} - 2\Delta f \), which depends on the exact deviation value.

Would you like more details on any of these calculations, or clarification on any part?

Here are 5 related questions you might want to explore:
1. How is the modulation index related to bandwidth in general for FSK?
2. What is the significance of frequency deviation in digital communication?
3. How would the adjacent frequencies change if the modulation index were different?
4. How can we calculate the exact bit rate once \( \Delta f \) is known?
5. What impact does bandwidth limitation have on FSK signal performance?

**Tip**: In FSK, a higher modulation index results in a larger frequency shift between the two states, which can affect bandwidth requirements.

Una señal digital se transmite empleando modulación FSK de 2 estados. El ancho de banda que ocupa la señal modulada es de 720 MHz y mantiene un índice de modulación igual a 8; con una portadora: S(t)=12Cos(25,133 x 10^9 t + 20);

Solve a digital signal modulation problem involving Frequency Shift Keying (FSK) with 720 MHz bandwidth and a modulation index of 8. This example uses key FSK formulas to determine adjacent frequencies, percentage frequency deviation, and signal transmission speed.

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