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Determine the values of power and energy of the following signals. Find whether signals are power, energy or neither energy nor power signals: $ x(n)=e^{j\left(\frac{\pi}{2} n+\frac{\pi}{4}\right)} $
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written 17 months ago by |
Solution:
$ x(n)=e^{j\left(\frac{\pi}{2} n+\frac{\pi}{4}\right)}\\ $
To find Energy of x(n):
$ \begin{aligned} E & =\sum_{n=-\infty}^{\infty}|x(n)|^2 \\\\ & =\sum_{n=-\infty}^{\infty} \mid e^{\left.j\left(\frac{\pi}{2} n+\frac{\pi}{4}\right)\right|^2} u(n)\\ \\ & =\sum_{n=-\infty}^{\infty}\left|e^{\left.j\left(\frac{\pi}{2} n+\frac{\pi}{4}\right)\right|^2} \quad \because\right| \\e^{j(\omega+\theta)} \mid=1 \\\\ & =\sum_{n=-\infty}^{\infty} 1=\infty \end{aligned} $
To find power of x(n):
$ \begin{aligned} P & =\lim _{n \rightarrow \infty} \frac{1}{2 …