Which statement correctly distinguishes a notch filter from a band-pass filter and includes the notch transfer function form?

• A. Notch (band-stop) attenuates a narrow band while passing others; H(s) can be written as H(s) = (s^2 + ω0^2)/(s^2 + (ω0/Q)s + ω0^2).
• B. Band-pass filters pass all frequencies equally.
• C. Notch filters are the same as high-pass filters with a tuned cutoff.
• D. Band-pass filters have a transfer function identical to the notch form.

Answer: (A)

Notch filters stop a narrow range of frequencies while letting frequencies outside that range pass with little attenuation. The transfer function given, H(s) = (s^2 + ω0^2) / (s^2 + (ω0/Q)s + ω0^2), makes this clear because the zeros are at s = ± jω0, so at the center frequency ω0 the numerator is zero and the magnitude response dips to zero (a notch). The denominator, with ω0 and Q, shapes how wide that notch is: a higher Q makes the notch narrower and the attenuation sharper, while a lower Q broadens it.

A band-pass filter, on the other hand, passes frequencies near a center frequency and attenuates others, rather than suppressing a specific narrow band. Its transfer function has a form that emphasizes frequencies around ω0 rather than introducing zeros on the imaginary axis at ± jω0. So the two types are fundamentally different in how they affect the frequency spectrum.

The other statements don’t fit because a band-pass does not pass all frequencies equally, a notch is not the same as a tuned high-pass, and a band-pass transfer function is not identical to the notch form.