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| + | [[Category:Formulas]] | ||
| + | |||
| + | keywords: energy, power, signal | ||
| + | |||
| + | <center><font size= 4> | ||
| + | '''[[Collective_Table_of_Formulas|Collective Table of Formulas]]''' | ||
| + | </font size> | ||
| + | |||
| + | '''Signal Metrics Definitions and Formulas''' | ||
| + | |||
| + | (used in [[ECE301]] and [[ECE438]]) | ||
| + | |||
| + | </center> | ||
| + | |||
| + | ---- | ||
| + | |||
{| | {| | ||
| − | |||
| − | |||
|- | |- | ||
! colspan="2" style="background: #eee;" | Metrics for Continuous-time Signals | ! colspan="2" style="background: #eee;" | Metrics for Continuous-time Signals | ||
|- | |- | ||
| − | | align="right" style="padding-right: 1em;" | CT signal energy ||<math>E_\infty=\int_{-\infty}^\infty | x(t) |^2 dt </math> | + | | align="right" style="padding-right: 1em;" | [[signal_energy_CT|(info)]] CT signal energy ||<math>E_\infty=\int_{-\infty}^\infty | x(t) |^2 dt </math> |
|- | |- | ||
| − | | align="right" style="padding-right: 1em;" | CT signal average power ||<math>P_\infty = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} \left | x (t) \right |^2 \, dt </math> | + | | align="right" style="padding-right: 1em;" | [[signal_power_CT|(info)]] CT signal (average) power ||<math>P_\infty = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} \left | x (t) \right |^2 \, dt </math> |
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | CT signal area ||<math>A_x = \int_{-\infty}^{\infty} x (t) \, dt </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Average value of a CT signal ||<math>\bar{x} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} x (t) \, dt </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | CT signal magnitude ||<math>M_x = \max_{-\infty<t<\infty} \left | x (t) \right | </math> | ||
|- | |- | ||
! colspan="2" style="background: #eee;" | Metrics for Discrete-time Signals | ! colspan="2" style="background: #eee;" | Metrics for Discrete-time Signals | ||
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|- | |- | ||
| align="right" style="padding-right: 1em;" | DT signal average power ||<math>P_\infty = \lim_{N \to \infty} \frac{1}{2N+1} \sum_{n=-N}^{N} \left | x [n] \right |^2 \, </math> | | align="right" style="padding-right: 1em;" | DT signal average power ||<math>P_\infty = \lim_{N \to \infty} \frac{1}{2N+1} \sum_{n=-N}^{N} \left | x [n] \right |^2 \, </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | DT signal area ||<math>A_x = \sum_{n=-\infty}^{\infty} x [n] \, </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Average value of a DT signal ||<math>\bar{x} = \lim_{N \to \infty} \frac{1}{2N+1} \sum_{n=-N}^{N} x [n] \, </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | DT signal magnitude ||<math>M_x = \max_{-\infty<t<\infty} \left | x [n] \right | </math> | ||
|- | |- | ||
|} | |} | ||
---- | ---- | ||
[[Collective_Table_of_Formulas|Back to Collective Table]] | [[Collective_Table_of_Formulas|Back to Collective Table]] | ||
| + | |||
[[Category:Formulas]] | [[Category:Formulas]] | ||
Latest revision as of 14:54, 25 February 2015
keywords: energy, power, signal
Signal Metrics Definitions and Formulas
| 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 | $ |
