Any signal can be decomposed into an overlapping sequence of grains

A continuous tone - or any audio signal - may be considered a sum of overlapping subquantities: a sequence of overlapping grains. The grains may be of arbitrary sizes and overlap amounts. Removing any grain changes the signal, confirming that each grain carries unique information. This completeness property is foundational to granular analysis-resynthesis: if grains span and overlap the entire signal, resynthesis from the grain set reconstructs the original. It also means granulation is not lossy in principle - only in implementation (windowing artifacts, quantization). The property underpins Gabor’s theory of acoustic quanta.

Examples

A 1-second sine tone can be decomposed into 100 overlapping Gaussian-windowed 30ms grains. Removing grain #47 leaves a gap in the resynthesized signal.

Assessment

What does it mean that grains form a complete representation of a signal? How does this property relate to the use of granular synthesis for pitch-time changing without quality loss?