3 - Jacobs University

I.
f MAX = 1Hz
I.
f MAX = 6Hz
II.
●
●
●
f S = 12Hz
II.
●
●
●
f S = 12Hz
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
III.
● ● ● ● ● ● ● ● ● ●
●
●
●
●
●
●
●
●
●
f S = 48Hz
III.
● ● ●
● ● ●
● ● ●
●
● ●
●
●
●
● ● ●
●
f S = 48Hz
●
●
●
●
●
●
●
●
●
●
● ● ● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ● ● ● ● ● ● ●
● ●
● ● ●
● ●
●
● ● ●
●
●
● ●
●
●
● ●
(a) Signal y(t) = sin (2πf 1 t) sampled at 12Hz and
48Hz respectively.
(b) Signal y(t) = sin (2πf 1 t) + 0.25 sin (2πf 2 t)
sampled at 12Hz and 48Hz respectively.
Figure 3: Sampling of two analog signals. In each of the two figures the uppermost plot presents
the continuous time signal (I.). Each signal was sampled using f S = 12Hz (II.) and f S = 48Hz
(III.). The signal on the left has one frequency component f 1 = f MAX = 1Hz, while the signal on
the right has two frequency components of f 1 = 1Hz and f 2 = f MAX = 6Hz respectively.
such as voltage or current, one may as well refer to any other quantity varying over time such
as the amount of money in a particular bank account measured in EUR or the level to which a
particular supplier production process fulfills the quality requirements of the outsourcing company
(process quality capability) measured in percent. In the discussion presented in this paper, we are
of course interested in the latter. Naturally such signals would exhibit variations on significantly
different time scale than electrical signals. Nevertheless, it is still possible to measure them on a
periodic basis to gain an idea about their overall behavior.
Usually a company would want to assess the quality capability of its suppliers and its variation
over time. The ability to identify any negative trends in the development of the quality capability
of their suppliers allows companies to detect and eliminate potential problems in a timely manner.
In this regard the quality audits could be deemed as the individual sampling measurements and
the sequence of audits at a particular supplier as the overall sampling signal. The average length
of the time intervals between individual quality audits would be therefore the ”sampling period”
T S = 1/f S .
11