Friday, October 25, 2019

Power or Energy Signal?


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=limN12N+1Nn=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=limN2N+12N+1=1


The signal x(n) has finite power and is consequently a "power signal".


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