SIGNAL CONDITIONING, DATA ACQUISITION, AND SPECTRAL ANALYSIS - Design and Development of Medical Electronic Instrumentation - page 236

information is made available. We explained above that according to Nyquist's theorem
the bare minimum sampling rate to avoid aliasing must be at least twice that of the high-
est-frequency component of the waveform. Because aliased components cannot be dis-
tinguished from real signals after sampling, aliasing is not just a minor source of error. It
is therefore of extreme importance that antialiasing fi filters with very high roll-off ff be used

for all serious spectral analysis.
Beyond appropriate sampling practices, the FFT still exposes other inherent traps which
can potentially make impossible the analysis of a signal. The most important of these prob-
lems are leakage and the picket-fence e

first problem is caused by the fact that
the FFT works on a short portion of the signal. This is called windowing because the FFT
can only see the portion of the signal that falls within its sampling “window,” after which
the FFT assumes that windowed data repeat themselves inde

ff ect. The fi

nitely. However, as shown in
Figure 5.17, this assumption is seldom correct, and in most cases the FFT analyzes a dis-
torted version of the signal that contains discontinuities resulting from appending win-
dowed data to their duplicates. In the PSD, these discontinuities appear as leakage of the
energy of the real frequency components into sidelobes that show up at either side of a
peak.
The second problem, called the picket-fence e

fi

ect or scalloping , is related inherently to
the discrete nature of the DFT. That is, the DFT will calculate the frequency content of a
signal at very well de

ff

ned discrete points in the frequency domain rather than producing
a continuous spectrum. Now, assuming a perfect system, if a certain component of the sig-
nal would have a frequency that falls between the discrete frequencies computed by the
DFT, this component would not appear in the estimated PSD.
To visualize this problem, suppose that an ideal signal is sampled at a rate of 2048 Hz
and processed through a 256-point FFT. There will then be a spectral channel every 4 Hz:
at dc, 4 Hz, 8 Hz, 12 Hz, and so on. Now suppose that the signal being analyzed is a pure

fi

Figure 5.17 A purely sinusoidal signal ( a ) has a single impulse as its true spectrum ( b ). However,
the signal is viewed by the FFT through a finite window ( c ), and it is assumed that this record is
repeated beyond the FFT's window ( d ). This leads to leakage of the main lobe to sidelobes in the
spectral estimate ( e ).