Can you tell me whether the following signal is a energy or power signal? x(n)=ej(nπ/2+π/8)
I've solved it and found it as it was neither power nor energy signal was that right?
Answer
The energy of a discrete-time signal is defined as
Ex=∞∑n=−∞|x(n)|2
and its power is given by
Px=limN→∞12N+1N∑n=−N|x(n)|2
With x(n)=ej(nπ/2+π/8) we have |x(n)|2=1 which implies that the sum in (1) does not converge, i.e. x(n) has infinite energy. For the power we get
Px=limN→∞2N+12N+1=1
The signal x(n) has finite power and is consequently a "power signal".
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