Question E7F08:
What is the function of decimation?  

Choices:  
A: Converting data to binary-coded decimal form  
B: Reducing the effective sample rate by removing samples  
C: Attenuating the signal  
D: Removing unnecessary significant digits    

Correct Answer is  B: Reducing the effective sample rate by removing samples  

To decimate is to lower the sampling rate by keeping only every M-th sample.

Why B is correct:
- Decimation reduces the sample rate by an integer factor $M$ by dropping samples:
  $$f_s' = \frac{f_s}{M} \quad \text{and} \quad x_d[n] = x[nM]$$
- In practice, you first low-pass filter (anti-alias) the signal, then keep every $M$-th sample.

Why the others are incorrect:
- A: Converting to binary-coded decimal is a data formatting task, not a sampling-rate change.
- C: While the anti-alias filter attenuates out-of-band components, the purpose of decimation is not general attenuation; it is sample-rate reduction.
- D: Removing significant digits is rounding/truncation (quantization), unrelated to sample-rate changes.

Useful formulas and rules of thumb:
- New sample rate after decimation by $M$:
  $$f_s' = \frac{f_s}{M}$$
- Always apply an anti-alias low-pass filter before downsampling:
  $$f_\text{cutoff} < \frac{f_s'}{2} = \frac{f_s}{2M}$$
- Example: $f_s = 48\ \text{kHz}$, $M=4$ ⇒ $f_s' = 12\ \text{kHz}$; keep every 4th sample.
- For large $M$, use multi-stage decimation to reduce filter complexity.