Week 6

Energy

The energy within an electric signal expressed by the function $f(x)$ may be expresseed as

\[E_x = \int_{-\infin}^{\infin}{|f(x)|^2 dx}\]

Periodic Signals

For a signal $x(t)=x(t+T)$,

• $T$ is the period
• $f=\frac{1}{T}$ is the frequency
• $\omega = 2\pi f$ is the angular frequency

Period of $\sin$ and $\cos$

The period of $\sin(k\pi)$ and $\cos(k\pi)$ is $\frac{2\pi}{k}$.

Compound Periods

If $p$ is a period of $f(x)$ and $g$ is any function, then $p$ is a period of $g(f(x))$.