Shorter time windows necessarily blur frequency knowledge in any signal

Evidence

The uncertainly principle states that the shorter the time signal, the broader the power spectrum in frequency. If we call the time uncertainty Δt, set by the autocorrelation duration, the frequency uncertainty Δf obeys … The uncertainty principle is one of the most important concepts in signal analysis. It thrusts itself into many situations, insisting that the shorter the time interval over which the sound is known or analyzed, the less is known about its frequency content. The time interval might be determined by the brevity of the recording or the window of time over which a recording is analyzed, but it equally well could be limited by the sound itself. If a trumpet player slides through a note in 1/20th of a second, it doesn’t matter whether the sound file itself lasts much longer, because that note’s frequency is actually not perfectly well-defined. According to the uncertainty principle, there is an intrinsic 20 Hz indeterminacy. — Eric J. Heller, Why You Hear What You Hear- An…, 416

Categorization

• XREF: Connects to the Heisenberg uncertainty principle in quantum mechanics — both are Fourier-pair consequences, not distinct phenomena. — connects to: Spectral analysis cannot achieve fine time and frequency resolution simultaneously — Almo Farina, Soundscape Ecology: Principles,…, 1970; Filtering a signal distorts its time response as well as its spectrum — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 473