Wavelet and constant-Q transforms trade time and frequency resolution non-uniformly

Evidence

Short-time Fourier analysis is a special case of a time–frequency representation. Other choices are wavelet analysis and Wigner distributions. In wavelet analysis (Cohen, 1995; Vetterli and Kovacevic, 1995), the frequency and time resolution are not uniform but vary so that at high frequencies the time resolution, is better with a coarser frequency resolution, and vice versa at low frequencies. A method related to wavelet processing is the constant-Q transform (Holighaus et al., 2013; Schörkhuber et al., 2013), where the signal is divided into time-frequency tiles of equal area, but the bandwidth increases with frequency to maintain a constant Q (Equation (3.30)). The temporal length of the tiles decreases with increasing frequency, which makes the processing a bit more complicated. However, perfect reconstruction processing has been achieved with constant-Q methods. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 394

Categorization

• XREF: Constant-Q transform links to how the auditory filter bank behaves — matching tonal perception — which connects to the cochlear/bark-scale content likely later in this same book.
• QUESTION: Why does the perceptual frequency scale justify a constant-Q (constant relative bandwidth) analysis rather than a linear one? The text asserts the motivation but does not spell out the psychoacoustic backing here.
• corroborated: 2 independent passages support this claim — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 394