Time and frequency resolution cannot both be improved simultaneously

Evidence

Ideally, we want to be able to see high-resolution data in the frequency and time domains simultaneously. Unfortunately, this is not always possible; in general, you can have one or the other, not both. Figure 9.11 illustrates some examples of the consequences of making different choices in frequency and time resolutions. — Toole, Floyd E, Sound reproduction- the acoustics and…, 951

Categorization

• QUESTION: The uncertainty principle tradeoff between frequency and time resolution in measurement — worth confirming the exact underlying math.
• corroborated: 2 independent passages support this claim — Toole, Floyd E, Sound reproduction- the acoustics and…, 951
• XREF: connects to: The time-energy uncertainty principle is really a time-frequency uncertainty principle in disguise — Eric J. Heller, Why You Hear What You Hear- An…, 434; Spectral and temporal resolution cannot both be maximized in any analysis; The ear’s time-frequency resolution cannot be modeled by fixed-length frames (+8 more)

Broader Connections

• Spectral and temporal resolution cannot both be maximized in any analysis #corroborates (0.95)
• The ear’s time-frequency resolution cannot be modeled by fixed-length frames #qualifies (0.80)
• Wavelet and constant-Q transforms use non-uniform time-frequency resolution unlike short-time Fourier analysis #exemplifies (0.80)
• The human hearing system compromises between frequency and time resolution, unlike ideal filters #exemplifies (0.75)
• Narrow-band equalization causes audible ringing in the time domain #exemplifies (0.75)
• Temporal resolution deficits, not frequency resolution, drive fine-structure processing failure #exemplifies (0.70)