Some General Purpose Formulas and Definitions
| General Purpose Formulas | |
|---|---|
| Euler's Formula and Related Equalities | |
| Euler's formula | $ e^{jw_0t}=\cos w_0t+j\sin w_0t $ |
| Cosine function in terms of complex exponentials | $ \cos\theta=\frac{e^{j\theta}+e^{-j\theta}}{2} $ |
| Sine function in terms of complex exponentials | $ \sin\theta=\frac{e^{j\theta}-e^{-j\theta}}{2j} $ |
| Function (or Signal) Metrics | |
| CT signal energy | $ E_\infty=\int_{-\infty}^\infty | x(t) |^2 dt $ |
| DT signal energy | $ E_\infty=\sum_{n=-\infty}^\infty | x[n] |^2 $ |
