Real signals contain smooth distributions of infinite frequencies

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)

So far we have mainly considered a sound wave to be a sinusoidal wave at a particular frequency. This is useful as it allows us to consider aspects of sound propagation in terms of the wavelength. However, most musical sounds have a waveform that is more complex than a simple sine wave; a variety of wave­ forms are shown in Figure 1.49. So how can we analyze real sound wave­ forms, and make sense of them in acoustical terms? The answer is based on the concept of superposition and a technique called Fourier analysis. — David Howard, Jamie Angus, coustics and Psychoacoustics, 436 (#expands, via linked claim)

Categorization

• XREF: connects to: Complex real-world sounds can be analyzed via Fourier analysis — David Howard, Jamie Angus, coustics and Psychoacoustics, 436; Accurate square waves require infinitely many harmonics; The Fourier transform pair converts signals between time and frequency domains — David Howard, Jamie Angus, coustics and Psychoacoustics, 440 (+1 more)

Broader Connections

• Accurate square waves require infinitely many harmonics #exemplifies (0.85)
• The Fourier transform pair converts signals between time and frequency domains #expands (0.80) — David Howard, Jamie Angus, coustics and Psychoacoustics, 440
• Complex real-world sounds can be analyzed via Fourier analysis #expands (0.78) — David Howard, Jamie Angus, coustics and Psychoacoustics, 436
• Non-linear and time-variant systems generate frequency components absent from the input #complicates (0.75) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 358