Phasors

$ x(t)=Ae^{j\theta+\phi} $

Where A is the radius of the phasor and $ \phi $ if the offset.

Useful Phasors Facts

$ e^{j\theta} = \cos{\theta}+j\sin{\theta} $

$ Ae^{j[\theta+\phi]}=Ae^{j\theta}e^{j\phi} $

$ \cos{\theta}=\frac{e^{j\theta}+e^{-j\theta}}{2} $

$ \sin{\theta}=\frac{e^{j\theta}-e^{-j\theta}}{2j} $

$ |e^{j\theta}|=1 $


Energy

Discrete

$ E_\infty = \sum_{n=-\infty}^\infty |x[n]|^2 $


Continuous

$ E_\infty = \int_{-\infty}^\infty |x(t)|^2\,dt) $


Power

Discrete

$ P_\infty = \lim_{N \to \infty} \left (\frac{1}{2N + 1} \sum_{n=-N}^{+N} |x[n]|^2 \right) $

Continuous

$ P_\infty = \lim_{T \to \infty} \left (\frac{1}{2T} \int_{-T}^T |x(t)|^2\,dt \right) $

Geometric Series

Alumni Liaison

Sees the importance of signal filtering in medical imaging

Dhruv Lamba, BSEE2010