*Question G8B10:
What is the relationship between transmitted symbol rate and bandwidth?*  

*Correct Answer is  B: Higher symbol rates require wider bandwidth*  

### AI Response: (may contain errors)  

The relationship between transmitted symbol rate and bandwidth is an important concept in digital communications. Let's break down the correct answer and why the other choices are incorrect:

### Correct Answer: B - Higher symbol rates require wider bandwidth

1. **Why the correct answer is correct:**
   - The symbol rate, often measured in baud, is the rate at which symbols are transmitted over a communication channel. Each symbol can represent multiple bits, depending on the modulation scheme.
   - According to the Nyquist theorem, the minimum bandwidth required to transmit a signal without intersymbol interference is directly proportional to the symbol rate. Therefore, as the symbol rate increases, the required bandwidth also increases to accommodate the faster transmission of symbols.

2. **Why the other choices are incorrect:**
   - **Choice A: Symbol rate and bandwidth are not related**
     - This is incorrect because there is a direct relationship between symbol rate and bandwidth. As explained, higher symbol rates necessitate wider bandwidths.
   - **Choice C: Lower symbol rates require wider bandwidth**
     - This is incorrect because lower symbol rates actually require less bandwidth, not more. The bandwidth requirement decreases as the symbol rate decreases.
   - **Choice D: Bandwidth is half the symbol rate**
     - This is incorrect because the bandwidth is not simply half the symbol rate. The relationship is more complex and depends on factors like the modulation scheme and filtering. For example, in a simple binary signaling system, the minimum bandwidth is approximately half the symbol rate, but this is not a general rule for all systems.

### Useful Formula

- **Nyquist Bandwidth Formula:**
  $$ B = \frac{R_s}{2} $$
  where:
  - $B$ = minimum bandwidth in hertz
  - $R_s$ = symbol rate in baud

This formula shows that the minimum bandwidth is proportional to the symbol rate, reinforcing that higher symbol rates require wider bandwidths.