Can you tell me whether the following signal is a energy or power signal? $$ x(n) = e^{j (n \pi/2 + \pi/8) } $$ I've solved it and found it as it was neither power nor energy signal was that right?
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2Can you show the work you did to arrive at your conclusion? I think this would be helpful in supplying an appropriate answer to your question. – user2718 May 31 '13 at 12:32
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The energy of a discrete-time signal is defined as
$$E_x=\sum_{n=-\infty}^{\infty}|x(n)|^2\tag{1}$$
and its power is given by
$$P_x=\lim_{N\rightarrow\infty}\frac{1}{2N+1}\sum_{n=-N}^{N}|x(n)|^2$$
With $x(n) = e^{j (n \pi/2 + \pi/8) }$ 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
$$P_x=\lim_{N\rightarrow\infty}\frac{2N+1}{2N+1}=1$$
The signal $x(n)$ has finite power and is consequently a "power signal".
Matt L.
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