The Gabor matrix tiles the time-frequency plane with acoustic quanta

Gabor proposed decomposing any sound into elementary acoustic quanta: Gaussian-windowed sinusoidal functions arranged on a rectangular lattice in the time-frequency plane. Each quantum (gaboret) has finite extent in both time and frequency, unlike Fourier sinusoids (infinite in time) or impulses (infinite in frequency). The matrix of these quanta tiles the time-frequency plane, providing a joint time-frequency representation analogous to the musical score. Each cell in the matrix captures the local energy at a specific time and frequency. This was the theoretical precursor to the short-time Fourier transform, the phase vocoder, and the wavelet transform.

Examples

The sonogram display in a DAW is a visual projection of the Gabor matrix: time on the horizontal axis, frequency on the vertical axis, amplitude as brightness.

Assessment

What is a Gabor acoustic quantum and how does it differ from a Fourier sinusoid? Explain why the Gabor matrix is described as a joint time-frequency representation.