*Question E7F09:
Why is an anti-aliasing filter required in a decimator?*  

*Correct Answer is  A: It removes high-frequency signal components that would otherwise be reproduced as lower frequency components*  

### AI Response: (may contain errors)  

To understand why an anti-aliasing filter is required in a decimator, let's break down the correct answer and the other choices.

### Correct Answer: A
**Why is this correct?**  
An anti-aliasing filter is used to remove high-frequency signal components before the decimation process. When you decimate (reduce the sampling rate) a signal, any frequency components above half the new sampling rate can be misrepresented as lower frequencies due to a phenomenon called aliasing. This can distort the signal and lead to incorrect interpretations. By filtering out these high-frequency components, we ensure that only the relevant frequencies are preserved, preventing aliasing.

### Incorrect Choices:
- **B: It peaks the response of the decimator, improving bandwidth**  
  This is incorrect because an anti-aliasing filter does not peak the response of the decimator. Instead, it is designed to attenuate high-frequency components. Peaking would imply enhancing certain frequencies, which is not the purpose of an anti-aliasing filter.

- **C: It removes low-frequency signal components to eliminate the need for DC restoration**  
  This is incorrect because the purpose of an anti-aliasing filter is not to remove low-frequency components. In fact, low-frequency components are typically the desired parts of the signal that we want to keep. DC restoration is a separate process that deals with offset issues in signals, not related to the function of an anti-aliasing filter.

- **D: It notches out the sampling frequency to avoid sampling errors**  
  This is incorrect because while it is important to avoid sampling errors, an anti-aliasing filter does not specifically notch out the sampling frequency. Instead, it focuses on removing frequencies above half the sampling rate (the Nyquist frequency) to prevent aliasing.

### Summary
- The anti-aliasing filter is crucial in a decimator to prevent high-frequency components from being misrepresented as lower frequencies.
- The other options either misrepresent the function of the filter or confuse it with other signal processing techniques.

### Key Concept
- **Nyquist Theorem**: To avoid aliasing, the sampling rate must be at least twice the highest frequency present in the signal. This is often summarized as:
$$ f_s \geq 2f_{max} $$
where:
- $f_s$ = sampling frequency
- $f_{max}$ = maximum frequency of the signal

This theorem underlines the importance of filtering out frequencies above the Nyquist limit before decimation.