DESIGN AND DEVELOPMENT OF MEDICAL ELECTRONIC ...

SAMPLING RATE AND THE NYQUIST THEOREM 225Figure 5.12 Nyquist stated that all the information needed to reconstruct a signal is provided by sampling at twice the highest signal frequencyat 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 betweenthe samples.The correct way of reconstructing a sampled signal is by using an interpolating filter. Thelow-pass reconstruction filter interpolates between the samples to make a smoothly varyingoutput signal. Let’s assume for a moment that the reconstruction filter is an ideal low-passfilter which has an infinitely steep cutoff. It eliminates all frequencies above the cutoff andhas no effect on either the amplitude of phase of frequencies below the cutoff. The impulseresponse of this low-pass filter is the sin function (sin x)/x. For the reconstruction, the stimulifed to this filter are the series of discrete impulses that are the original digitized samples.Every time an impulse hits the filter, it “rings”—and it is the superposition of all these peakyrings that reconstructs the proper signal. If the signal contains frequency components thatare close to one-half the sampling rate, the reconstruction filter has to be very sharp indeed.This means that it will have a very long impulse response—long enough to fill in the signaleven in region of the low-amplitude samples.Channel skew is another issue that must be considered when establishing how to sampledata. Channel skew is the undesirable effect of time-shifting sampled data points thatotherwise should be time aligned. Let’s assume that you are sampling multiple biopotentialsignals acquired from the same source through an electrode array. Take, for example,the signals displayed in Figure 1.33, which were recorded differentially using 32 surfaceelectrodes placed 2.54 mm apart over the biceps brachii muscle. A proper sampling rate forthese signals is about 10 kHz. Sequential sampling of the 32 channels would result in a