Time-Invariant and Time-Varying Systems

A system is called time-invariant if a time shift (delay or advance) in the input signal
causes the same time shift in the output signal. Thus, for a continuous-time system, the
system is time-invariant if
for any real value of T. For a discrete-time system, the system is time-invariant (or
shift-invariant ) if

~ { x [-nk ] ) =y[n - k ] (1.72)

for any integer k. A system which does not satisfy (continuous-time system) or(discrete-time system) is called a time-varying system. To check a system for
time-invariance, we can compare the shifted output with the output produced by the
shifted input