SIGNAL CONDITIONING, DATA ACQUISITION, AND SPECTRAL ANALYSIS - Design and Development of Medical Electronic Instrumentation - page 225

Figure 5.12 Nyquist stated that all the information needed to reconstruct a signal is provided by sampling at twice the highest signal fre-
quency at least, which does not imply that the samples will look like the signal. ( a ) A 48-Hz signal ( b ) is sampled at 100 Hz (circles). ( c )
Simply drawing lines between the samples does not reconstruct the original signal.

signal, but the correct reproduction is not achieved just by drawing straight lines between
the samples.
The correct way of reconstructing a sampled signal is by using an interpolating fi filter. The

low-pass reconstruction filter interpolates between the samples to make a smoothly varying

output signal. Let's assume for a moment that the reconstruction

fi

fi filter is an ideal low-pass

fi filter which has an in fi nitely steep cutoff ff . It eliminates all frequencies above the cutoff ff and

has no e ff ect on either the amplitude of phase of frequencies below the cutoff. ff . The impulse

response of this low-pass fi filter is the sin function (sin x )/ x . For the reconstruction, the stim-

uli fed to this filter are the series of discrete impulses that are the original digitized samples.

Every time an impulse hits the

fi

filter, it “rings”—and it is the superposition of all these peaky
rings that reconstructs the proper signal. If the signal contains frequency components that
are close to one-half the sampling rate, the reconstruction

fi

filter has to be very sharp indeed.
This means that it will have a very long impulse response—long enough to

fi

fi fill in the signal

even in region of the low-amplitude samples.
Channel skew is another issue that must be considered when establishing how to sam-
ple data. Channel skew is the undesirable e

ect of time-shifting sampled data points that
otherwise should be time aligned. Let's assume that you are sampling multiple biopoten-
tial signals acquired from the same source through an electrode array. Take, for example,
the signals displayed in Figure 1.33, which were recorded di

ff

erentially using 32 surface
electrodes placed 2.54 mm apart over the biceps brachii muscle. A proper sampling rate for
these signals is about 10 kHz. Sequential sampling of the 32 channels would result in a

ff