Any complex tone is decomposable into sine wave components displayed as a spectrum

Evidence

In general, as the rise time gets faster and/or the corners get sharper, more high-frequency sine waves are required to represent the waveform accurately. In other words, we can look at a square wave as a waveform that is formed by summing together sine waves that are odd multiples of its fundamental frequency and whose amplitudes are inversely proportional to frequency. … This representation is called the frequency domain representation, or spectrum, of a waveform, and the waveform’s amplitude versus time plot is called its time domain representation. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 449

Categorization

• DEFINE: Defines the core distinction between frequency domain (spectrum) and time domain representations of any waveform.
• XREF: connects to: Any waveform can be exactly modeled by combining sine waves — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 443; Any complex waveform can be decomposed into simple sine waves — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 439; Sine waves of varying frequency, amplitude, and phase can construct any waveform — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 446 (+8 more)

Broader Connections

• Any complex waveform can be decomposed into simple sine waves #corroborates (0.98) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 439
• Sine waves of varying frequency, amplitude, and phase can construct any waveform #corroborates (0.98) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 446
• Any complex waveform can be built from independent orthogonal sine waves #corroborates (0.97)
• Sine waves are the simplest periodic excitation, and all complex waveforms decompose into them #corroborates (0.97) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 135
• A square wave is built from odd-multiple sine components #exemplifies (0.90) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 449
• Any periodic signal decomposes into harmonic sinusoids at integer multiples of a fundamental frequency. #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2732
• Any waveform can be approximated by summing orthogonal sine waves #qualifies (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 440
• A waveform’s sharpness dictates how many high-frequency sine waves it contains #expands (0.78)
• Sound spectrum analysis depends on banks of filters to decompose signals #expands (0.75)
• Almost every musical sound contains at least two frequency components #exemplifies (0.72)