Audio Principles 5is inversely proportional to the frequency. It is easy to remember that the wavelength of
1000 Hz is a foot (about 30 cm).
1.3 Periodic and Aperiodic Signals .................................................................................
Sounds can be divided into these two categories and analyzed either in the time domain
in which the waveform is considered or in the frequency domain in which the spectrum is
considered. The time and frequency domains are linked by transforms of which the best
known is the Fourier transform.
Figure 1.3(a) shows that an ideal periodic signal is one which repeats after some constant
time has elapsed and goes on indefi nitely in the time domain. In the frequency domain
such a signal will be described as having a fundamental frequency and a series of
harmonics or partials that are at integer multiples of the fundamental. The timbre of an
instrument is determined by the harmonic structure. Where there are no harmonics at all,
the simplest possible signal results that has only a single frequency in the spectrum. In the
time domain this will be an endless sine wave.
Figure 1.3(b) shows an aperiodic signal known as white noise. The spectrum shows that
there is an equal level at all frequencies, hence the term “ white, ” which is analogous to
the white light containing all wavelengths. Transients or impulses may also be aperiodic.
A spectral analysis of a transient [ Figure 1.3(c) ] will contain a range of frequencies, but
these are not harmonics because they are not integer multiples of the lowest frequency.
Generally the narrower an event in the time domain, the broader it will be in the
frequency domain and vice versa.
WavelengthWavelengthFigure 1.2 : Wavelength is defi ned as the distance between two points at the same place on
adjacent cycles. Wavelength is inversely proportional to frequency.