Civil Engineering Reference
In-Depth Information
Applying DFT analysis however, we see that the sound (or noise), being mainly
stochastic, also contain periodic components (pure tones). The measuring technique
using fixed bandwidth filters will also give correct RMS-values for these pure tone
must be less than the distance between the pure tone components and 2) the rest of the
signal inside the band must be negligible. The frequency resolution will however be poor
and without the ability to repeat the analysis using another bandwidth it is difficult to
decide whether or not a periodic component is present in the signal.
Without doubt, we may by looking at the one-third-octave band data in
Figure 1.13
be reasonably sure that there are pure tones around 250 Hz and 1000 Hz but this is not so
around 2000 Hz. Using DFT gives quite another opportunity to detect such components
1.4.5.2
FFT analysis
The breakthrough concerning the use of the discrete Fourier transform (DFT) came with
the finding of an algorithm for a fast calculation, giving the fast Fourier transform (FFT).
is of the order of milliseconds for many thousands of samples. The number of channels
available in one instrument has also steadily increased. This offers the opportunity to
map the global motion of a whole system in just one operation as opposed to using a
single channel instrument capable of measuring at just one point at the time.
Many of the examples shown here are calculated using an FFT routine. It may be
pertinent at this point to sum up the deliberations one must make before starting an
analysis, this in spite of the “brain” the instrument maker has put into the instrument.
One may normally choose the number of samples
N
(1024, 2048, 4096, ...) or from
a limited set. The next choice to decide on is the maximum frequency
f
max
. This normally
results in setting the sampling frequency
f
s
to a minimum value of 2⋅
f
max
(a common
choice is 2.56⋅
f
max
). Furthermore, the anti-aliasing filter of the instrument is set to “cut
away” all frequency components above
f
max
. What will the frequency resolution then be?
From section
1.4.4
we know that the frequency lines will be
nn
nf
s
f
=
=
=
where
n
=
0, 1, 2, 3,...,
N
−
1.
n
TNt
Δ
N
As an example we may choose
N
= 1024 and
f
max
to be 5000 Hz. With
f
s
= 2.56 ⋅
f
max
=
12800 Hz, the total time of analysis
T
will be 80 milliseconds. The number of frequency
lines below the Nyquist frequency will then be 512 with a frequency resolution Δ
f
= 12.5
Hz. A commercial instrument will then present a total of 400 lines, i.e. all lines up to the
chosen maximum frequency, 400⋅12.5 Hz = 5000 Hz. An alternative choice of
N
= 2048
will give 800 lines with a resolution of 6.25 Hz and so on.
This kind of analysis, called
base band analysis
, gives lines from 0 Hz to
f
max
. More
often, one is interested in zooming in on a smaller frequency interval, which means that
one would like to have all frequency lines
f
n
inside an interval given by
f
1
<
f
n
<
f
2
. Most
instruments have this option but imply that one must repeat the measurement. More
details concerning this technique may be found in the rather extensive literature on the
subject.
2
The analysis is performed using a Hanning window, which gives good accuracy as for the frequency of the
pure tone but less accuracy when it comes to amplitude.
