MANUAL OF ANALOGUE SOUND RESTORATION ... - British Library

BOX 2.3
THE POWER-BANDWIDTH PRODUCT IN AUDIO RECORDINGS
This box is aimed at engineers. It is relatively easy to assess the informationcarrying
capacity of analogue devices such as transformers, landlines, and
satellites. They tend to have flat responses within the passband, Gaussian noise
characteristics, and clear overload points. But sound recordings generally do
not have these features, so I must explain how we might quantify the powerbandwidth
product of sound recordings.
Analogue media overload “gently” - the distortion gradually gets worse as
the signal volume increases. So we must make an arbitrary definition of
“overload.” In professional analogue audio circles, two percent total harmonic
distortion was generally assumed. As this is realistic for most of the analogue
media we shall be considering, I propose to stick to this.
For electronic devices, the bandwidth is conventionally assumed to be the
points where the frequency response has fallen to half-power. This is distinctly
misleading for sound recordings, which often have very uneven responses; the
unevenness frequently exceeds a factor of two. There is another complication
as well (see section 2.4). For my purposes, I propose to alter my definition of
“bandwidth” to mean the point at which the signal is equal to random
(Gaussian) noise - a much wider definition. Yet this is not unrealistic, because
random noise is in principle unpredictable, so we can never neutralise it. We
can only circumvent it by relying upon psychoacoustics or, for particular
combinations of circumstances (as we shall see in Chapter 3). Thus random
noise tends to form the baseline beyond which we cannot go without
introducing subjectivism, so this definition has the advantage that it also forms
the limit to what is objectively possible.
But most recording media do not have Gaussian noise characteristics. After
we have eliminated the predictable components of noise, even their random
noise varies with frequency in a non-Gaussian way. We must perform a
spectral analysis of the medium to quantify how the noise varies with
frequency. And because we can (in principle) equalise frequency-response
errors (causing an analogous alteration to the noise spectrum), the difference
between the recorded frequency-response and the noise-spectrum is what we
should measure.
The human ear’s perception of both frequencies and sound-power is a
“logarithmic” one. Thus, every time a frequency is doubled, the interval sounds
the same (an “octave”), and every time the sound power increases by three
decibels the subjective effect of the increase is also very similar to other threedecibel
increases. Following the way analogue sound engineers work, my
assessment of the power-bandwidth product of an analogue sound recording is
therefore to plot the frequency response at the 2% harmonic-distortion level,
and the noise spectrum, on a log-log graph; and measure the AREA between
the two curves. The bigger the area, the more information the recording holds.
15