Frequency, phase, and impulse responses are interchangeable transforms of each other

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: Impulse velocity response serves as a ready-made autocorrelation; Impulse response analysis replaces mode analysis once mode density gets high.; A signal’s autocorrelation is a cosine sum over its sinusoidal partials. (+7 more)

Related

• Certain processes are far easier to analyze in the frequency domain than in time (similarity 0.89)
• The Fourier transform pair converts signals between time and frequency domains (similarity 0.85)
• Frequency-domain thinking makes filtering easier than time-domain (similarity 0.84)
• The Fourier transform measures how a signal matches each sinusoid pair (similarity 0.83)
• Filtering operates as multiplication in the frequency domain, a key spectral analysis technique (similarity 0.83)
• Time-frequency transforms make signal processing and interpretation easier (similarity 0.83)
• Real signals contain smooth distributions of infinite frequencies (similarity 0.83)
• The Fourier transform trades costly time-domain convolution for simple frequency-domain multiplication (similarity 0.82)
• Impulse velocity response serves as a ready-made autocorrelation (similarity 0.80)
• Frequency and time domain representations equivalently define linear loudspeaker behavior (similarity 0.80)
• The Fourier transform unwinds periodic signals into flat DC (similarity 0.79)
• Complex real-world sounds can be analyzed via Fourier analysis (similarity 0.79)
• A signal’s autocorrelation is a cosine sum over its sinusoidal partials. (similarity 0.79)
• Every wave-like quantity has an uncertainty principle tying its Fourier transform pair (similarity 0.78)

Broader Connections

• The Fourier transform pair converts signals between time and frequency domains #expands (0.95) — David Howard, Jamie Angus, coustics and Psychoacoustics, 440
• An all-pass filter alters phase and timing but not amplitude #exemplifies (0.75)