A high‐resolution time–frequency representation for musical instrument signals

Analyzing musical signals to obtain the time‐varying magnitudes and frequencies of instruments’ partial frequency components is important for resynthesis, transcription, and instrument physics. Windowing techniques, including Fourier series extensions, short‐time Fourier transforms, and constant‐Q transforms, generate bias in time and frequency dictated by the uncertainty principle. This is significant to analysis requirements of such properties as attack, which involve changes over millisecond time ranges and require frequency accuracy on the order of cents. Alternatives such as the Wigner distribution avoid the uncertainty principle restriction and associated bias, but nonlinear cross products of magnitude and frequency computations are not smoothed as with windowing methods, increasing those sources of bias. All these techniques belong to Cohen’s class, a framework where this paper develops the modal distribution, exhibiting decreased total bias. Computation of the modal distribution and a constant‐Q v...