I can't figure out how to get the magnitudes for periodic discrete Fourier transforms.
For example if $x[n] = cos(\frac{\pi}{4}n + \frac{\pi}{2})$, I need to find and plot the magnitude $|X(e^{jw})|$ and the angle. I think I got that $X(e^{jw}) = \sum_{k=-\infty}^{+\infty}\frac{j}{2}[2\pi \delta(\omega - \frac{\pi}{4} - 2\pi k) + 2\pi \delta(\omega + \frac{\pi}{4} - 2\pi k)]$ although I'm not sure if this is correct. Then I think I learned that for discrete FTs since they are always periodic with period $2\pi$ you just pay attention to the values between $-\pi$ and $\pi$. So I get for the FT, two impulses of area $j\pi$ at +-$\frac{\pi}{4}$. Then I need to figure out the magnitude and angle of this? I'm stuck on this part and also not sure if I got the FT correct in the first place. Any help is appreciated, thanks.