Filter selectivity — “The less selective a filter is, the steeper the slope (sharper the roll-off) at its cutoff frequencies.” Is this statement accurate?

Introduction / Context:Selectivity describes how well a filter separates passband from stopband. It is tightly linked to roll-off steepness, transition bandwidth, and quality factor (Q). This question tests whether you can correctly relate selectivity and slope at the cutoff region.

Given Data / Assumptions:

• Standard low-pass/high-pass/band-pass/band-stop filters.
• Slope discussed in dB/decade or dB/octave per order.

Concept / Approach:Greater selectivity corresponds to sharper transition regions and steeper skirts. Higher-order filters (or higher Q for resonant responses) achieve steeper roll-off, which improves selectivity. Therefore, a filter that is “less selective” has gentler slopes and broader transition regions, not steeper ones.

Step-by-Step Solution:

Verification / Alternative check:Bode plots of Butterworth/Chebyshev/Elliptic filters show that tighter selectivity comes with steeper roll-off (or ripples/zeros) near cutoff.

Why Other Options Are Wrong:

Common Pitfalls:Confusing passband flatness with selectivity; assuming “less selective” equals “more slope,” which reverses the real relationship.

Final Answer:False