Introduction to signals - Continuous and Discrete Time Signals and Systems - page 59

Fig. P1.29. ECG pattern for
Problem 1.29.

1.2

0.8

0.4

0

−0.4

−0.8

0 0.5 1 1.5 2

time (s)

2.5 3 3.5

Sketch the following signals expressed as a function of x 1 [ k ] and x 2 [ k ]:
(i) x 1 [ k ];
(ii) x 2 [ k ];
(iii) x 1 [3 − k ];
(iv) x 1 [6 − 2 k ];
(v) x 1 [2 k ];

(vi) x 2 [3 k ];
(vii) x 1 [ k / 2];
(viii) x 1 [2 k ] + x 2 [3 k ];
(ix) x 1 [3 − k ] x 2 [6 − 2 k ];
(x) x 1 [2 k ] x 2 [ − k ].

1.29 In most parts of the human body, a small electrical current is often pro-
duced by movement of different ions. For example, in cardiac cells the
electric current is produced by the movement of sodium (Na

+

) and potas-

+

sium (K ) ions (during different phases of the heart beat, these ions enter

or leave cells). The electric potential created by these ions is known as an
ECG signal, and is used by doctors to analyze heart conditions. A typical
ECG pattern is shown in Fig. P1.29.
Assume a hypothetical case in which the ECG signal corresponding to
a normal human is available from birth to death (assume a longevity of
80 years). Classify such a signal with respect to the six criteria mentioned
in Section 1.1. Justify your answer for each criterion.

1.30 It was explained in Section 1.2 that a complicated function could be
represented as a sum of elementary functions. Consider the function f ( t )
in Fig. P1.26. Represent f ( t ) in terms of the unit step function u ( t ) and
the ramp function r ( t ).

1.31 (M ATLAB exercise) Write a set of M ATLAB functions that compute and
plot the following CT signals. In each case, use a sampling interval of
0.001 s.