Contents
Practice Question on Computing the Fourier Transform of a Discrete-time Signal
Compute the Fourier transform of the signal
$ x[n] = \cos \left( \frac{\pi}{6}n \right).\ $
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
$ \cos \left( \frac{\pi}{6}n \right)=\frac{1}{2}e^{j\frac{\pi}{6}n}+\frac{1}{2}e^{-j\frac{\pi}{6}n} $
$ \mathcal X (\omega)=\sum_{m=-\infty}^\infty 2\pi \delta (\omega-k\omega_0+2\pi m) $
$ \mathcal X (\omega)=\sum_{m=-\infty}^\infty 2\pi \delta (\omega-\frac{\pi}{6}+2\pi m)+\sum_{m=-\infty}^\infty 2\pi \delta (\omega+\frac{\pi}{6}+2\pi m) $
--Cmcmican 19:51, 28 February 2011 (UTC)
Answer 2
Write it here.
Answer 3
Write it here.
