Any continuous signal decomposes into sinusoidal partials and convolution simplifies in frequency domain

Evidence

Any signal that meets certain continuity requirements can be represented with arbitrary precision as a sum of sinusoidal components of different frequencies. These components are often called partials. … An important advantage of using the Fourier transform is that it converts the computationally expensive convolution in the time domain into a much simpler multiplication in the frequency domain. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 372

Categorization

• DEFINE: Explains why the Fourier approach is central to all audio processing: decomposition into partials plus the convolution-to-multiplication trick are the load-bearing ideas.