Born-Jordan time-frequency analysis (Harmonic Analysis and Nonlinear Partial Differential Equations)

Abstract

Born-Jordan quantization originates from the early quantum mechanics, leading to sharp time-frequency localization of signals. The related Born-Jordan transform provides an attractive alternative to short-time Fourier transform. We review the essential time-frequency analysis, characterizing the Born-Jordan transform within Cohen s class, and show how all this works in audio signal processing. Computationally, our Born-Jordan approach is as complex as using spectrograms (which suffer from arbitrariness of chosen analysis window, resulting in inferior localization). We relate this to singular integral operators, and compare the Weyl quantization to the Born-Jordan case.