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If I set tow M-PSK signals: Symbol clock at 8.3k sym/s M=4 and M=8. Also, set two M-QAM signals: Symbol clock at 8.3k sym/s M=4 and M=8.What is the first-null bandwidth of this signal?

To determine the **first-null bandwidth** of each of these signals, let's use the symbol rate and the modulation types specified. The first-null bandwidth for **M-PSK** and **M-QAM** signals is related to the **symbol rate** and the **modulation type**.

### Definitions and Formulas:
1. **First-null bandwidth for M-PSK signals**:
   \[
   B = 2 \times \text{Symbol Rate} = 2 \times f_s
   \]
   where \( f_s \) is the symbol rate.

2. **First-null bandwidth for M-QAM signals**:
   Similar to PSK, the bandwidth of a QAM signal also has a first-null bandwidth given by:
   \[
   B = 2 \times f_s
   \]

Given:
- **Symbol Rate (Symbol clock)**: \( f_s = 8.3 \, \text{k symbols/s} = 8.3 \, \text{kHz} \)
- **Modulation types**: M-PSK (M = 4 and M = 8), M-QAM (M = 4 and M = 8)

Since the bandwidth for both M-PSK and M-QAM signals is twice the symbol rate, we can compute the first-null bandwidth for each:

### Calculations:
1. **4-PSK (M = 4) and 8-PSK (M = 8)**:
   \[
   B_{\text{PSK}} = 2 \times 8.3 \, \text{kHz} = 16.6 \, \text{kHz}
   \]

2. **4-QAM (M = 4) and 8-QAM (M = 8)**:
   \[
   B_{\text{QAM}} = 2 \times 8.3 \, \text{kHz} = 16.6 \, \text{kHz}
   \]

### Summary:
- The **first-null bandwidth** for both **4-PSK** and **8-PSK** is **16.6 kHz**.
- The **first-null bandwidth** for both **4-QAM** and **8-QAM** is also **16.6 kHz**.

These results apply because the first-null bandwidth only depends on the symbol rate and not directly on the modulation order \( M \) in this case.

Would you like further clarification on these calculations or additional examples? 

Here are some related questions for practice:
1. What would the bandwidth be if the symbol rate changed to 10 kHz?
2. How does changing the modulation order affect the data rate?
3. What are the main differences between QAM and PSK modulation in terms of spectral efficiency?
4. How is bandwidth efficiency calculated for these modulation schemes?
5. Why does QAM modulation allow for amplitude variation while PSK does not?

**Tip:** In PSK and QAM, the symbol rate and bandwidth have a linear relationship in the simplest cases, but spectral efficiency improves with higher modulation schemes (higher \( M \)).

If I set two M-PSK signals: Symbol clock at 8.3k sym/s M=4 and M=8. Also, set two M-QAM signals: Symbol clock at 8.3k sym/s M=4 and M=8. What is the first-null bandwidth of this signal?

Learn how to calculate the first-null bandwidth for M-PSK and M-QAM signals. This solution uses a symbol rate of 8.3k sym/s and explores modulation schemes with M = 4 and M = 8. Understand the relationship between symbol rate, PSK, QAM, and bandwidth in digital communication.

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