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Determine whether the signals are power or energy signals. Calculate energy/power accordingly:
1 Answer
written 8.5 years ago by | • modified 6.4 years ago |
(i) x(t)=0.9e−3tu(t)
E=∞∫−∞|x(t)|2dt
=∞∫−∞|0.9e−3tu(t)|2dt=0.81∞∫0e−6tdt=0.81[e−6t−6]∞0=0.81/6E=0.135J
Since the signal is not periodic hence it’s not a power signal but it is a energy signal.
(ii) x[n]=u[n]
The signal is periodic because u(n) repeats after every sample and of infinite duration.
Hence it is a Power Signal
P=limN→∞12N+1N∑−N|x[n]|2=limN→∞12N+1N∑−N|u[n]|2=limN→∞12N+1N∑0(1)2
Since N∑0(1)2=1+1+1+⋯∞=(N+1)P=limN→∞12N+1(N+1)=limN→∞N(1+1N)N(2+1N)=0.5W.P=0.5W