Question E7F02:
What kind of digital signal processing audio filter is used to remove unwanted noise from a received SSB signal?  

Choices:  
A: An adaptive filter  
B: A crystal-lattice filter  
C: A Hilbert-transform filter  
D: A phase-inverting filter    

Correct Answer is  A: An adaptive filter  

To remove random noise on received SSB audio, DSP radios use an adaptive filter.

Why A is correct (Adaptive filter):
- An adaptive filter continuously adjusts its coefficients to minimize noise while preserving speech. This is the basis of DSP “NR” (noise reduction) in many HF rigs.
- Common approach: least-mean-squares (LMS) adaptation that minimizes the output error power.

Key LMS relations:
- Desired signal: $d(n)$ (noisy speech), input vector: $x(n)$
- Filter output: $y(n) = \mathbf{w}^T \mathbf{x}(n)$
- Error: $e(n) = d(n) - y(n)$
- Coefficient update: $$\mathbf{w}_{n+1} = \mathbf{w}_n + \mu\, e(n)\, \mathbf{x}(n)$$
- Rule of thumb: choose small $\mu$ for stability; larger $\mu$ converges faster but can distort speech.

Why the others are incorrect:
- B: Crystal-lattice filter
  - Fixed, analog IF filter for selectivity (bandwidth/shape factor). It doesn’t adapt to changing noise and isn’t an audio DSP noise reducer.
- C: Hilbert-transform filter
  - Provides a 90° phase shift over a band; used in the phasing method of SSB generation/demod (I/Q), not for noise reduction.
- D: Phase-inverting filter
  - Produces 180° phase shift; used in balanced/phasing applications, not to suppress random audio noise.

Useful rules of thumb:
- Adaptive NR is most effective on random (uncorrelated) noise; less effective on strong, narrowband interferers (use notch/IF filtering for carriers).
- Moderate NR settings preserve intelligibility; excessive NR can introduce artifacts.