Good frequency resolution and good time resolution can never coexist

Evidence

Thus all filters have a time response which is a function of the fre­ quency range or bandwidth of the signals that they pass. Note that this is an inherent problem that cannot be solved by technology. The time response of a filter is inversely proportional to the bandwidth so a narrowband filter has a slow rise and fall time whereas a wide-band filter has faster rise and fall times. In practice this effect means that if the frequency resolution of the spectral analysis is good, implying the use of narrowband analysis filters, then the time response is poor and there is significant smearing of the signal. On the other hand if the time response is good then the frequency resolution will be poor, because the filter bandwidths will have to be wider. — David Howard, Jamie Angus, coustics and Psychoacoustics, 482

Categorization

• DEFINE: Clarifies the fundamental time-bandwidth tradeoff that is the core of all spectral analysis.
• XREF: Connects to quantum uncertainty and to Gabor’s work on time-frequency uncertainty in acoustics. — connects to: Spectral analysis cannot achieve fine time and frequency resolution simultaneously — Almo Farina, Soundscape Ecology: Principles,…, 1970