Question E7F03:
What type of digital signal processing filter is used to generate an SSB signal?  

Choices:  
A: An adaptive filter  
B: A notch filter  
C: A Hilbert-transform filter  
D: An elliptical filter    

Correct Answer is  C: A Hilbert-transform filter  

To generate an SSB signal using DSP, the phasing method uses a Hilbert-transform filter to create a 90° phase-shifted version of the audio. This allows one sideband to cancel while the other remains.

Why C (Hilbert-transform filter) is correct:
- A Hilbert transform produces a frequency-dependent phase shift of ±90° with flat amplitude, exactly what the phasing method needs.
- Create two audio signals: $x(t)$ and its Hilbert transform $\hat{x}(t)$ (90° shifted).
- Mix them with quadrature RF carriers and sum/difference to cancel one sideband.

Useful formulas:
- Hilbert transform (time domain): $\hat{x}(t) = x(t) * \left(\frac{1}{\pi t}\right)$
- Frequency-domain property: multiplies by $-j\,\text{sgn}(f)$, giving a 90° phase shift.
- Phasing method SSB:
  - $$s_{\text{USB}}(t) = x(t)\cos(2\pi f_c t) - \hat{x}(t)\sin(2\pi f_c t)$$
  - $$s_{\text{LSB}}(t) = x(t)\cos(2\pi f_c t) + \hat{x}(t)\sin(2\pi f_c t)$$

Why the other choices are incorrect:
- A: Adaptive filter — adapts coefficients to changing signals/noise; not specifically for generating SSB.
- B: Notch filter — removes a narrow tone; unrelated to forming SSB sidebands.
- D: Elliptical filter — a steep band-pass/low-pass type used when filtering is the method; not the DSP phasing method’s core element.

Rules of thumb:
- “Hilbert = 90° phase shift = SSB phasing method.”
- Sum/difference with quadrature carriers selects USB or LSB by cancellation.