Convolution mathematically links LTI system inputs to outputs.

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 (#expands, via linked claim)

The recorded compound action potential (CAP ) is described as the convolution of the unit response (UR , i.e., the waveform resulting from a single action potential) with the compound discharge latency distribution (CDLD ), the sum of spike events over time of all individual nerve fibres (Goldstein and Kiang 1958 , see also Fig. 1 ). — Dijk, Pim van, Physiology, Psychoacoustics and…, 2383 (#exemplifies, via linked claim)

With certain parameter values the model of the string sounds like a guitar not an acoustic guitar, but an electric guitar. This happens because the model does not include the model of the body of the guitar. The model of the body can be implemented simply by convolving the output of the string model with a measured impulse response of the guitar body shown in Figure 6.3. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 697 (#exemplifies, 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; Population latency distributions become Gaussian after convolution across many fibres; Anechoic recordings produce the best spatialized audio when convolved with HRIRs (+7 more)

Broader Connections

• The Fourier transform trades costly time-domain convolution for simple frequency-domain multiplication #expands (0.95) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 373
• A compound action potential equals single-fibre waveform convolved with spike latency distribution #exemplifies (0.90) — Dijk, Pim van, Physiology, Psychoacoustics and…, 2383
• Population latency distributions become Gaussian after convolution across many fibres #exemplifies (0.85)
• Auditory masking spread can be modelled by convolving with a spreading function #exemplifies (0.85)
• Frequency-domain thinking makes filtering easier than time-domain #expands (0.85)
• A guitar body’s effect can be simulated by convolution with its measured impulse response #exemplifies (0.85) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 697
• Human hearing is highly nonlinear and cannot be LTI-modelled beyond peripheral parts #qualifies (0.85)
• Anechoic recordings produce the best spatialized audio when convolved with HRIRs #exemplifies (0.80)
• Deconvolution of compound responses reveals two firing components invisible in raw waveforms #exemplifies (0.80)
• Signal processing compensates reproduction deviations through equalization #exemplifies (0.75)