Building Acoustics

28 Building acoustics

The literature on MLS is relatively large but for a discussion of basic properties one
may look at the article by Rife and Vanderkooy (1989). Summing up we may state the
following: The MLS is a periodic binary sequence having an approximately flat
spectrum. Such sequences are easily generated using an arrangement of shift registers.
The length L of a sequence is given by

L= 21 m− , (1.30)

where m is the number of steps in the shift register, a number that also denotes the order
of the sequence. One may generate several sequences of the same order but each of them
is unique. An example is shown in Figure 1.22, being the first 65 samples of a sequence
of order 12. The whole length is thereby 4095. In practice sequences up to the order of
20–22 are used, i.e. a length of several millions.

0 10 20 30 40 50 60

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Sample number

Amplitude

Figure 1.22 Example of maximum length sequence (MLS). The first 65 samples of a sequence of order 12.

When listening to such a sequence and a common white noise signal played
through a loudspeaker, it is very difficult to distinguish between them. Technically, they
are used in the same way. The MLS is however, not only deterministic but assuming it is
replayed periodically, we will get a line spectrum with a distance between lines given by

s (Hz),

f

f

L

Δ= (1.31)

where fs is the sampling frequency, i.e. the fixed rate of outputting the binary samples.
Using a sampling frequency of 10 000 Hz the time for outputting a sequence of order 12
will be 0.41 seconds. One therefore has the ability to adapt the signal to the given task by
choosing sequence length and sampling frequency. The main advantage is, however, the
deterministic property; we may repeat the measurement many times to improve the
accuracy of the measured variable. This is true only when assuming the system to be
constant during the measurement; the system must be time invariant. As pointed out