Filtering in the frequency domain is simply multiplicative on spectra

Evidence

The effect of a filter on a spectrum is multiplicative in that the output spectrum after filtering is the product of the filter’s frequency response with the input signal’s spectrum. Thus we can easily determine the effect of a given filter on a signal’s spectrum. This is a useful technique which can be applied to the analysis of musical instruments, as we shall see later, by treating some of their characteristics as a form of filtering. In fact, filtering can be carried out using mechanical, acoustical and electrical means, and many instruments perform some form of filtering on the sounds they generate (see Chapter 4). — David Howard, Jamie Angus, coustics and Psychoacoustics, 470

Categorization

• DEFINE: Conveys the key frequency-domain property that makes filter analysis tractable: multiplication, not convolution.
• XREF: Connects to the idea that physical and mechanical systems (e.g., ear canal, instruments) act as filters — links to psychoacoustic resonance chapters. — connects to: Filtering a signal distorts its time response as well as its spectrum — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 473
• SEED: Angle: treating the human body itself (pinna, ear canal) as a filter bank — the body’s frequency response shapes all perception of sound.