Resonance peaks always require compensating anti-resonant valleys in the spectrum

Evidence

Suppose we have a body that extends to infinity and returns no echoes. The power as a function of frequency will be smooth, and forms a reference level. If echoes and resonances are induced by adding structures and boundaries some distance away, resonances will develop, enhancing the power at certain frequencies. The average power theorem dictates that resonance peaks must rob Peter to pay Paul; resonance peaks must be compensated by nearby dips where the power is lower—that is, anti-resonant valleys. The power averaged over large enough frequency intervals must equal the power that would be delivered if the echoes and their resonances didn’t exist. — Eric J. Heller, Why You Hear What You Hear- An…, 1092

Categorization

• XREF: Conservation-of-spectral-energy principle echoes discussions of ‘robbing Peter to pay Paul’ in frequency-domain constraints elsewhere.