The Fourier transform trades costly time-domain convolution for simple frequency-domain multiplication

Evidence

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…, 373

Categorization

• DEFINE: Explains the convolution theorem mechanism that underpins digital signal processing efficiency.
• XREF: Connects to how convolution reverbs and filtering are implemented in audio software; also the reason FFT is everywhere in acoustic analysis. — connects to: Convolution mathematically links LTI system inputs to outputs.; The Fourier transform pair converts signals between time and frequency domains — David Howard, Jamie Angus, coustics and Psychoacoustics, 440; Filtering operates as multiplication in the frequency domain, a key spectral analysis technique (+2 more)
• corroborated: 3 independent passages support this claim — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 373

Broader Connections

• The Fourier transform pair converts signals between time and frequency domains #expands (0.85) — David Howard, Jamie Angus, coustics and Psychoacoustics, 440
• Filtering operates as multiplication in the frequency domain, a key spectral analysis technique #exemplifies (0.80)
• Frequency-domain thinking makes filtering easier than time-domain #qualifies (0.75)
• A loudspeaker array’s polar pattern is a Fourier transform of its illumination #exemplifies (0.75)