Wavelet and constant-Q transforms use non-uniform time-frequency resolution unlike short-time Fourier analysis
Evidence
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
Category: Definitional Content
- DEFINE: Defines wavelet analysis and the constant-Q transform in contrast to frame-based spectrograms.