Biomedical Signal Processing - Computational Intelligence in Biomedical Engineering - page 19

2.2.2 Sampling and Analog Reconstruction
Many digital systems are obtained by sampling an analog system to obtain
discrete values at fixed time intervals, usually denoted by T . The motivation
for digitization includes greater functionality and reproducibility, more modu-
larity and flexibility, better performance (Stein, 2000), and convenient storage.
Digitization requires proper signal representation so that minimal signal infor-
mation is lost, hence the goal of sampling is to obtain a digital representation
of the analog signal accurate enough to reconstruct the original. Sampling can
be performed by passing the analog signal x ( t ) through a switch that allows
certain points of the analog waveform through when turned on. The sampling
frequency can be controlled by a control signal (Figure 2.5), which controls the
frequency of the switch operation. Since analog signals can have a range of fre-
quencies the sampling has to be performed carefully. For example, if the analog
signal has low frequency, then we would sample it at larger time intervals and
vice versa. Unfortunately, the disadvantage of digitization is the introduction
of noise or high-frequency components in the power spectra of the signal.
To minimize this, the input analog signal x ( t ) is bandlimited with cutoff
frequency f C . The sampling theorem then states that the sampling frequency,
f SR , should be at least twice the cutoff or maximum frequency, f C , that is,

f SR ≥ 2 f C (2.11)

The minimum sampling rate is known as the Nyquist rate, where the Nyquist
frequency is defined as

f NR = f SR
2

(2.12)

so that the Nyquist intervals for a signal frequency f are then uniformly
defined as

f − f SR

2

<f<f + f SR
2

(2.13)

X

X ( t )

S ( t )

FIGURE 2.5
Analog to digital signal conversion using sampling where switch X is turned
on and off by the control signal S ( t ). (Adapted from Winter, D.A. and
Palta, A.E., Signal Processing and Linear Systems for the Movement Sciences ,
Water1oo Biomechanics, Waterloo, Canada, 1997.)