keywords: energy, power, signal

Collective Table of Formulas

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 | $

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