Introductory concepts - Practical Biomedical Signal Analysis Using MATLAB - page 5

FIGURE 1.1: Illustration of sampling and interpolating of signals. a) The continu-
ous signal (gray) is sampled at points indicated by circles. b) The impulse response of
the Whittaker-Shannon interpolation formula for a selected point. c) Reconstruction
(black) of signal computed according to (1.14).

1.2.1.1 Aliasing

What happens if the assumption of the sampling theorem is not fulfilled and the
original signal contains frequencies higher than the Nyquist frequency? In such cases
we observe an effect called aliasing —different signal components become indistin-
guishable (aliased). If the signal of frequency f 0

F s is sampled with fre-
quency F s then it has the same samples as the signal with frequency f 1

∈ 2 F s

,

= F s − f 0 .

1
2 F s . The sampled signal contains additional low frequency com-
ponents that were not present in the original signal. An illustration of that effect is
shownin Figure1.2.

Note that | f 1 | <

1.2.2 Quantization error
When we measure signal values, we usually want to convert them to numbers
for further processing. The numbers in digital systems are represented with a finite
precision. The analog to digital converter (ADC) is characterized by the number of
bits N it uses to represent numbers. The full range R of measurement values is divided
into 2 N

R
2 N (Figure

levels. The quantization error can be estimated as being less than

1.3).
This error sometimes has to be taken into consideration, especially when the am-
plitudes of measured signals span across orders of magnitude. An example here can
be EEG measurement. Let's assume that we have adjusted the amplification of signal