Civil Engineering Reference
In-Depth Information
easily and accurately determine impulse responses for a system and thereby one may
determine the corresponding transfer functions. The method is widely used in building
acoustics, in room acoustic measurements as well as in measurements of sound
insulation. In recent years, however, the swept sine technique has become a rival to the
technique using MLS (see below). An important feature in both methods is the larger
dynamic range as compared with earlier conventional methods.
White noise
h(
τ
)
Cross-
correlation
SYSTEM
Figure 2.3
Principle determination of the impulse response of a system by cross correlation.
The measurement principle using MLS is based on the fact that when using a
stochastic white noise input signal one will obtain the impulse response when cross
correlating the output and input signals. The principle set-up is shown in
Figure 2.3.
The
crucial point is that one may get an accurate estimate of the impulse response by
substituting the white noise signal with an MLS signal. Since the latter is deterministic
one may, assuming as before that the system is time invariant, constantly improve the
estimate by increasing the number of sequences used in the averaging process.
Obtaining the impulse response using the swept sine technique may be
implemented in different ways. Maybe the simplest one to grasp is the one illustrated in
Figure 2.4,
where one as a first step performs a Fourier transform of both the output and
the input signal. By a spectral division we obtain the transfer function directly, and the
impulse response may be obtained by an inverse Fourier transform. As pointed out in
Chapter 1 the swept sine technique has some important advantages compared with the
technique using MLS, e.g. more robust in terms of time variance and an even greater
dynamic range may be obtained.
MLS or SS
SYSTEM
FFT
h(
τ
)
IFFT
FFT
Figure 2.4
Principle determination of the impulse response of a system by spectral division of the Fourier
transforms.
2.3.3
Examples of transfer functions. Mechanical systems
A transfer function is certainly linked to the specific variables defined as being the
excitation (input) and the response (output). In acoustics and vibration there are a number
