Werbung
Verfügbare Sprachen
Verfügbare Sprachen
FFT analysis
General information
The principal applications
for fast Fourier transform analysis
are in the fields of mechanics and mechanical engineering,
for structural and vibration analysis. FFT analysis is also
used in the audio and acoustics fields, as well as in general
electronic applications in which complicated signals need
to be illuminated. Oscilloscopes can be used to measure
changes in signal amplitude over a certain period of time
{in Yt mode).
However,
the harmonic
content
of the
waveform cannot usually be captured, or if at ali, then only
within certain
narrow
limits. The FFT analysis function
provided by this part of the program permits the data from
a Yt test signal to be processed in such a way that harmonic
analysis can
be performed.
The signal
data
(sampled
points) from the scope are converted
to the frequency
range, thus yielding a spectrum of discrete harmonics. The
Discrete Fourier Transform
(DFT) supplies a harmonic
spectrum that is symmetrical with respect to the sampling
frequency and contains N/2 spectral lines equidistant from
one another. When using the scope to capture signals for
analysis, it is important to record several complete signal
repetitions; the minimum number required will depend on
the specific waveform.
This
increases
accuracy
while
reducing socalled "leakage errors" (see graphic). Errors of
this kind lead to inaccuracies both in the cursor- supported
frequency display and in the amplitude display. If a signal
is captured by the scope at an excessively low sampling
rate, then
socalled
aliasing
effects
can
occur:
false
harmonics not contained in the signal are displayed. The
highest theoretically capturable frequency can be derived
with the aid of the sampling theorem. It must be smaller
than half the actual sampling frequency.
Discontinuity errors can be avoided with the aid of various
window functions (in the evaluation function) that can be
selected as appropriate for the measurement problem at
hand.
At the same
time, they result in a compromise
between the resolution and the accuracy of the amplitude
display of the harmonic spectrum. When analyzing single-
shot events
(transients), only the square-wave
window
function may be used.
The amplitude accuracy is always slightly off; the cause of
these errors is inherent in the measurement system itself.
The smaller the signal amplitude
being evaluated, the
greater is the impact of the +/- 1/2 LSB conversion error of
the scope's
57
Werbung
