Question E7C11:
Which of the following measures a filter’s ability to reject signals in adjacent channels?  

Choices:  
A: Passband ripple  
B: Phase response  
C: Shape factor  
D: Noise factor    

Correct Answer is  C: Shape factor  

Correct answer: C — Shape factor

Why it’s correct:
- Shape factor quantifies how “steep” a filter’s skirts are, which directly relates to rejecting adjacent-channel signals.
- Defined as the ratio of the bandwidth at a higher attenuation to the bandwidth at a lower attenuation:
  $$SF = \frac{BW_{A_2}}{BW_{A_1}}$$
  Commonly:
  $$SF = \frac{BW_{60\,\text{dB}}}{BW_{6\,\text{dB}}} \quad \text{or} \quad \frac{BW_{40\,\text{dB}}}{BW_{3\,\text{dB}}}$$
- Lower shape factor (closer to 1) means steeper skirts and better adjacent-channel rejection.

Why the others are incorrect:
- Passband ripple (A): Describes amplitude variation within the passband (e.g., peak-to-peak ripple in dB). It does not measure skirt steepness or adjacent-channel rejection.
- Phase response (B): Describes phase vs. frequency; impacts group delay and signal distortion, not adjacent-channel rejection.
- Noise factor (D): Measures SNR degradation:
  $$F = \frac{SNR_{in}}{SNR_{out}}, \quad NF = 10\log_{10}F \; \text{dB}$$
  It relates to noise performance, not selectivity in adjacent channels.

Rules of thumb:
- Better adjacent-channel rejection ⇔ lower shape factor.
- Example: If a CW filter has $BW_{6\,\text{dB}} = 500\ \text{Hz}$ and $BW_{60\,\text{dB}} = 800\ \text{Hz}$,
  $$SF = \frac{800}{500} = 1.6 \quad \text{(good)}$$
- High-quality crystal/roofing filters often have $SF \lesssim 2:1$.