Signals with autocorrelations that decay to zero need continuous spectra
Evidence
By way of contrast and to complete the story, sounds that have no definite musical pitch (but a pitch nevertheless—see what follows) associated with them, such as the “ss” in sea (Figure 3.9 later in the chapter), have an acoustic pressure waveform that does not repeat regularly, and is often random in its variation with time and is therefore not periodic. Such a waveform is referred to as being “aperiodic” (see Chapter 1). The spectrum of such sounds contains frequency components that are not related as integer multiples of some frequency, and there are no harmonic components. The spectrum will often contain all frequencies, in which case it is known as a “continuous” spectrum. An example of an acoustic pressure waveform and spectrum for a nonperiodic sound is illustrated in Figure 3.6 for a snare drum being brushed. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 822 (
#expands, via linked claim)
Thus the main difference between the spectrum of periodic and aperiodic waveforms is that periodic waveforms have discrete partials, which can be represented as lines in the spectrum with a spacing that is inversely proportional to the period of the 7F Hz 5F Hz 3. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 460 (
#expands, via linked claim)
Categorization
- XREF: connects to: Periodic and aperiodic spectra differ in discrete versus continuous partials — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 460; Periodic sounds give line spectra while aperiodic sounds give continuous spectra — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 822
Broader Connections
- Periodic sounds give line spectra while aperiodic sounds give continuous spectra
#expands(0.90) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 822 - Periodic and aperiodic spectra differ in discrete versus continuous partials
#expands(0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 460