*Question E7F10:
What aspect of receiver analog-to-digital conversion determines the maximum receive bandwidth of a direct-sampling software defined radio (SDR)?*  

*Correct Answer is  A: Sample rate*  

### AI Response: (may contain errors)  

To determine the maximum receive bandwidth of a direct-sampling software defined radio (SDR), the key factor is the sample rate.

### Correct Answer: Sample Rate

- **Explanation**: The Nyquist theorem states that to accurately sample a signal without aliasing, the sample rate must be at least twice the highest frequency component of the signal. Therefore, the maximum bandwidth that can be received is directly related to the sample rate. If the sample rate is $f_s$, the maximum bandwidth $B$ is given by:

$$
B = \frac{f_s}{2}
$$

This means that if you want to capture a signal with a certain bandwidth, you need to ensure your sample rate is at least double that bandwidth.

### Why Other Choices Are Incorrect

- **B: Sample Width in Bits**: 
  - The sample width (or bit depth) affects the resolution and dynamic range of the signal but does not directly determine the maximum bandwidth. It influences how accurately the amplitude of the signal can be represented but not the frequency range that can be captured.

- **C: Integral Non-Linearity**: 
  - This refers to the deviation of the actual output from the ideal output in an analog-to-digital converter (ADC). While it can affect the accuracy of the conversion, it does not limit the maximum bandwidth of the receiver.

- **D: Differential Non-Linearity**: 
  - Similar to integral non-linearity, differential non-linearity describes how well the ADC maintains a consistent step size between quantization levels. It impacts the performance of the ADC but does not set a limit on the maximum bandwidth.

### Summary

- The maximum receive bandwidth of a direct-sampling SDR is determined by the sample rate, as per the Nyquist theorem. The other factors, while important for the quality and accuracy of the signal processing, do not limit the bandwidth.