Building Acoustics

22 Building acoustics

0 100 200 300 400 500

Frequency (Hz)

1E-006

1E-005

1E-004

1E-003

1E-002

G

(f

), relative values

n = 5

n = 25

n = 100

Figure 1.17 Power spectrum (relative values) calculated by averaging n time samples of the type shown in
Figure 1.16, using N = 1024 and fs = 1000 Hz. Note: The curves are shifted by a factor of 10.

1.5 Analysis in the time domain. Test signals

We have up to now concentrated on the frequency domain description of various types of
oscillation (represented by signals). We have, starting out from a description in the time
domain, made a transformation into the frequency domain, which is the most common
way of describing sound and vibration phenomena. In some situations there are,
however, other types of information that is required such as the statistical amplitude
distribution or the autocorrelation function, the latter giving information on the
dependence of data obtained at different times. It is reasonable in this context also to give
some examples of this matter.
We have treated rather thoroughly the subject of stochastic noise, assuming a
Gaussian distribution. The reason for this is partly due to the common use of such signals
as test signals when measuring various types of transfer function. These are measurement
situations where we want to map the relationship between a physical quantity
representing the input to the system and another physical quantity representing the output
or the response. This could be the velocity at a point in mechanical system excited by a
force at the same point or at a more distant point. As another example, it could be the
sound pressure level at a given position in a room when a given voltage is applied to the
input terminals of a loudspeaker. The topic of transfer functions and applications is
treated in the next chapter. Here we shall use a stochastic noise signal as an illustration of
time signal analysis and further present a couple of deterministic signal types, also
popular as test signals.