Question E8C04:
What technique minimizes the bandwidth of a PSK31 signal?  

Choices:  
A: Zero-sum character encoding  
B: Reed-Solomon character encoding  
C: Use of sinusoidal data pulses  
D: Use of linear data pulses    

Correct Answer is  C: Use of sinusoidal data pulses  

To minimize PSK31 bandwidth, the waveform’s transitions are smoothed so they don’t splatter energy into adjacent frequencies.

Why C (Use of sinusoidal data pulses) is correct
- PSK31 shapes each symbol with a sinusoidal (often sin²) phase/pulse shape so the phase transition is gradual and its derivative is continuous. This suppresses keying sidebands and concentrates energy near the carrier.
- With proper shaping, the occupied bandwidth is roughly the symbol rate:
  $$BW \approx R$$
  For PSK31, $R = 31.25$ baud, so the occupied bandwidth is on the order of 31 Hz.

Why the other choices are incorrect
- A: Zero-sum character encoding
  - Encoding choice does not spectrally shape the waveform. PSK31 uses Varicode to improve efficiency and reduce long runs, but that affects throughput, not instantaneous occupied bandwidth.
- B: Reed-Solomon character encoding
  - FEC adds redundancy to improve error correction; it does not narrow the signal. If anything, it increases the number of symbols sent for the same information, potentially broadening the effective occupancy over time.
- D: Use of linear data pulses
  - Linear ramps still have slope discontinuities at the start/end of symbols, producing more spectral sidelobes than sinusoidal shaping. Sinusoidal shaping provides smoother transitions and better sidelobe suppression.

Useful formulas and rules of thumb
- Abrupt/rectangular keying produces a sinc spectrum with large sidelobes:
  $$|H(f)| \propto \mathrm{sinc}(fT)$$
  where $T$ is symbol time.
- Bandwidth is inversely related to rise time:
  $$BW \approx \frac{0.35}{t_r}$$
  Smoother (longer, sinusoidal) transitions increase $t_r$ and reduce occupied bandwidth/splatter.
- For well-shaped PSK (like PSK31):
  $$BW \approx R \quad \text{(with low sidelobes due to sinusoidal shaping)}$$