Filtering operates as multiplication in the frequency domain, a key spectral analysis technique

Evidence

Fourier further theorized that if he combined enough sine waves together he could exactly model any waveform in existence. This allowed him to develop the Fourier transform pair—two equations that provide a means of transforming the time domain into the frequency domain and back. — David Howard, Jamie Angus, coustics and Psychoacoustics, 440 (#expands, via linked claim)

Categorization

• XREF: connects to: The Fourier transform trades costly time-domain convolution for simple frequency-domain multiplication — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 373; Signal processing compensates reproduction deviations through equalization; Certain processes are far easier to analyze in the frequency domain than in time (+2 more)

Broader Connections

• Filtering a spectrum is multiplicative, so instrument characteristics can be modeled as filters. #expands (0.95)
• The Fourier transform pair converts signals between time and frequency domains #expands (0.75) — David Howard, Jamie Angus, coustics and Psychoacoustics, 440