Question E8A06:
What is the approximate ratio of PEP-to-average power in an unprocessed single-sideband phone signal?  

Choices:  
A: 2.5 to 1  
B: 25 to 1  
C: 1 to 1  
D: 13 to 1    

Correct Answer is  A: 2.5 to 1  

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In unprocessed SSB voice, the speech waveform has peaks that rise several dB above the average. The typical crest factor is about 4 dB, which corresponds to a PEP-to-average power ratio of about 2.5:1.

Useful relationships:
- Power ratio from dB:  
  $$\text{Power ratio} = 10^{(\text{dB}/10)}$$
- For 4 dB:  
  $$10^{(4/10)} \approx 2.51 \Rightarrow \text{PEP} \approx 2.5 \times \text{Average power}$$

Why A (2.5 to 1) is correct:
- Unprocessed SSB speech commonly has a crest factor of about 4 dB, giving $PEP/P_{\text{avg}} \approx 2.5$. A practical rule of thumb: average output is about 40% of PEP with no processing.

Why the others are incorrect:
- B: 25 to 1  
  - $$10\log_{10}(25) \approx 14\ \text{dB}$$  
  - Far too high for typical unprocessed speech; would imply extremely peaky audio.
- C: 1 to 1  
  - 0 dB crest factor; would require a constant-envelope or heavily processed signal, not normal SSB voice.
- D: 13 to 1  
  - $$10\log_{10}(13) \approx 11.1\ \text{dB}$$  
  - Also much higher than expected for unprocessed SSB speech.

Rule of thumb:
- Unprocessed SSB: $PEP/P_{\text{avg}} \approx 2.5:1$ (about 4 dB).
- Speech processing/compression reduces crest factor, raising average power closer to PEP.