Discussion
What limits how sharply a practical filter can cut off?
Answer: A
Two things together. An infinitely sharp cut-off would require a non-causal impulse response, one that responds before the input arrives, so it cannot be realised at all; and every degree of approach to it costs filter order, which means components, loss, group-delay ripple and cost. The practical design therefore trades transition width against complexity and against phase behaviour in the passband. The sampling theorem constrains the sampling rate rather than the filter. The following stage's noise figure matters to sensitivity but not to achievable selectivity. And impedance affects matching rather than the shape of the response.
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