Page 66 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 11 SlGNALS AND SYSTEMS 55

1.59. Give an example of a system that satisfies the condition of homogeneity (1.67) but not the
condition of additivity (1.66).
Ans. Consider the system described by

1.60. Give an example of a linear time-varying system such that with a periodic input the correspond-
ing output is not periodic.
Ans. y[n] = T{x[n]) = m[n]

1.61. A system is called invertible if we can determine its input signal x uniquely by observing its
output signal y. This is illustrated in Fig. 1-43. Determine if each of the following systems is
invertible. If the system is invertible, give the inverse system.

X Y Inverse x -
System
system

Fig. 1-43

Ans. (a) Invertible; x(t)= iy(r)
(b) Not invertible
dy(0
(c) Invertible; x(t ) = -
dt
(d) Invertible; x[n] = y[n] - y[n - 11
(el Not invertible