keywords: energy, power, signal

Signal Metrics Definitions and Formulas

(used in ECE301 and ECE438)

Metrics for Continuous-time Signals
(info) CT signal energy $E_\infty=\int_{-\infty}^\infty | x(t) |^2 dt$
(info) CT signal (average) power $P_\infty = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} \left | x (t) \right |^2 \, dt$
CT signal area $A_x = \int_{-\infty}^{\infty} x (t) \, dt$
Average value of a CT signal $\bar{x} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} x (t) \, dt$
CT signal magnitude $M_x = \max_{-\infty<t<\infty} \left | x (t) \right |$
Metrics for Discrete-time Signals
DT signal energy $E_\infty=\sum_{n=-\infty}^\infty | x[n] |^2$
DT signal average power $P_\infty = \lim_{N \to \infty} \frac{1}{2N+1} \sum_{n=-N}^{N} \left | x [n] \right |^2 \,$
DT signal area $A_x = \sum_{n=-\infty}^{\infty} x [n] \,$
Average value of a DT signal $\bar{x} = \lim_{N \to \infty} \frac{1}{2N+1} \sum_{n=-N}^{N} x [n] \,$
DT signal magnitude $M_x = \max_{-\infty<t<\infty} \left | x [n] \right |$

## Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal