A square wave is built from odd-multiple sine components

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. A sine wave represents a single frequency, and therefore a sine wave of a given amplitude can be plotted as a single line on a graph of amplitude versus frequency. The components of a square wave plotted in this form are shown in Figure 1.51, which clearly shows that the square wave consists of a set of progressively reducing discrete sine wave components at odd multiples of the lowest 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: Establishes the time-domain vs frequency-domain (spectrum) distinction — foundational terminology for the whole book.
• XREF: Frequency domain vs time domain reappears constantly in audio analysis and DSP; connects to Fourier’s theorem also discussed in this book. — connects to: Any waveform can be exactly modeled by combining sine waves — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 443; Any complex tone is decomposable into sine wave components displayed as a spectrum — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 449