Question E7F04:
Which method generates an SSB signal using digital signal processing?  

Choices:  
A: Mixing products are converted to voltages and subtracted by adder circuits  
B: A frequency synthesizer removes unwanted sidebands  
C: Varying quartz crystal characteristics are emulated in digital form  
D: Signals are combined in quadrature phase relationship    

Correct Answer is  D: Signals are combined in quadrature phase relationship  

Correct answer: D — Signals are combined in quadrature phase relationship

1) Why D is correct
- In DSP, SSB is commonly generated by the phasing (I/Q) method. You create two versions of the modulating signal: the in‑phase part, m(t), and a 90° phase‑shifted (Hilbert transform) part, ˆm(t). You then mix them with carrier signals that are also 90° apart and combine to cancel one sideband.
- USB and LSB forms:
  - Upper sideband:
    $$s_{USB}(t) = m(t)\cos(2\pi f_c t) - \hat{m}(t)\sin(2\pi f_c t)$$
  - Lower sideband:
    $$s_{LSB}(t) = m(t)\cos(2\pi f_c t) + \hat{m}(t)\sin(2\pi f_c t)$$
- Complex/baseband view:
  $$s(t) = \Re\{[m(t) + j\hat{m}(t)]\,e^{j2\pi f_c t}\}$$
  The quadrature combination suppresses one sideband.

2) Why the other choices are incorrect
- A: Mixing products are converted to voltages and subtracted by adder circuits  
  - Mixers already produce RF/IF sum and difference frequencies; “converting mixing products to voltages and subtracting” is not the recognized DSP SSB method. The key is 90° (quadrature) relationships and Hilbert transforms, not generic subtraction of “mixing products.”
- B: A frequency synthesizer removes unwanted sidebands  
  - Synthesizers generate stable LO frequencies; they do not remove sidebands. Sideband suppression requires filtering or quadrature combination.
- C: Varying quartz crystal characteristics are emulated in digital form  
  - While DSP can implement filters analogous to crystal filters (the “filter method”), SSB is not produced by “varying quartz crystal characteristics.” The description is inaccurate for DSP; the classic DSP method in exams is the quadrature (phasing) approach.

3) Useful formulas and rules of thumb
- Hilbert transform creates the needed 90° phase shift:
  $$\hat{m}(t) = \mathcal{H}\{m(t)\}$$
- USB/LSB via I/Q:
  - USB: combine as $m\cos - \hat{m}\sin$
  - LSB: combine as $m\cos + \hat{m}\sin$
- Rule of thumb: If you see “DSP” and “SSB,” think “I/Q (quadrature) generation using a Hilbert transform” to cancel one sideband. Frequency synthesizers do not remove sidebands.