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So many symbols, so little time... Here's a quick lookup table for our commonly-used symbols!  
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=List of Symbols=
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So many symbols, so little time... Here's a quick lookup table for our commonly-used symbols in [[ECE]], especially [[ECE301]] and [[ECE438]]!  
 
*<math>\omega_s</math>: Sampling frequency; equal to <math>\frac{2\pi}{T}</math>
 
*<math>\omega_s</math>: Sampling frequency; equal to <math>\frac{2\pi}{T}</math>
 
*<math>\omega_m</math>: Maximum frequency in a band-limited signal (<math> = max(\{|w|\ :\ w \neq 0\})</math>
 
*<math>\omega_m</math>: Maximum frequency in a band-limited signal (<math> = max(\{|w|\ :\ w \neq 0\})</math>
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*<math>X(s)</math>: The Laplace Transform of <math>x(t)</math>.
 
*<math>X(s)</math>: The Laplace Transform of <math>x(t)</math>.
 
The above symbols are brought to you with thanks to Brian Thomas
 
The above symbols are brought to you with thanks to Brian Thomas
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<h3>Signal Metrics</h3>
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<br/>
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<ul style="list-style:none;">
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  <li><strong>Signal Energy</strong>
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    <ul style="list-style:none;">
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      <li>
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        <p><math>E_x = \int_{-\infty}^{\infty} |x(t)|^2\,dt</math> for ct (continuous time)</p>
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        <p><math>E_x = \sum_{n=-\infty}^{\infty} |x(n)|^2</math> for dt (discrete time)</p>
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      </li>
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    </ul>
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  </li>
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  <li><strong>Signal Power</strong>
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    <ul style="list-style:none;">
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      <li>
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        <p><math>P_x = \lim_{T \Rightarrow \infty}\frac{1}{2T}\int_{-T}^{T} |x(t)|^2\,dt</math> for ct (continuous time)</p>
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        <p><math>P_x = \lim_{N \Rightarrow \infty}\sum_{n=-N}^{N} |x(n)|^2</math> for dt (discrete time)</p>
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        <p>note: for periodic signals <br/>
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        <math>P_x = \frac{1}{N}\sum_{n=0}^{N-1}|x(n)|^2</math>
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        </p>
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      </li>
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    </ul>
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  </li>
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  <li><strong>Signal RMS (root-mean-square)</strong>
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    <ul style="list-style:none;">
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      <li>
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      <math>X_{rms} = \sqrt{P_x}</math>
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      </li>
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    </ul>
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  </li>
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  <li><strong>Signal Magnitude</strong>
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    <ul style="list-style:none;">
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      <li>
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        <p><math>m_x = max|x(t)|</math>, for CT</p>
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        <p><math>m_x = max|x(n)|</math>, for DT</p>
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        <p> if <math>m_x < \infty</math>, we say signal is bounded</p>
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      </li>
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    </ul>
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  </li>
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----
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[[ECE|Back to ECE]]
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 +
[[ECE301|Back to ECE 301]]
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 +
[[ECE438|Back to ECE 438]]

Latest revision as of 11:08, 12 November 2010

List of Symbols

So many symbols, so little time... Here's a quick lookup table for our commonly-used symbols in ECE, especially ECE301 and ECE438!

  • $ \omega_s $: Sampling frequency; equal to $ \frac{2\pi}{T} $
  • $ \omega_m $: Maximum frequency in a band-limited signal ($ = max(\{|w|\ :\ w \neq 0\}) $
  • $ \omega_c $: Cutoff frequency of a filter ($ \omega_c > 0 $). (For instance, lowpass filters are nonzero in the range $ \omega \in [-\omega_c, \omega_c] $.)
  • $ T $: Sampling period; equal to $ \frac{2\pi}{\omega_s} $
  • NR, or "Nyquest Rate": $ =2\omega_m $. If $ \omega_s > NR = 2\omega_m $, then the band-limited signal can be uniquely reconstructed from the sampled signal.
  • $ p(t) $: "Impulse train" -- equivalent to $ \sum_{n=-\infty}^{\infty} \delta(t-nT) $
  • $ s $: A complex number -- often expressed as a sum of it's parts, $ a+j\omega $, where $ a, \omega \in \mathbb{R} $
  • $ X(s) $: The Laplace Transform of $ x(t) $.

The above symbols are brought to you with thanks to Brian Thomas

Signal Metrics


  • Signal Energy
    • $ E_x = \int_{-\infty}^{\infty} |x(t)|^2\,dt $ for ct (continuous time)

      $ E_x = \sum_{n=-\infty}^{\infty} |x(n)|^2 $ for dt (discrete time)

  • Signal Power
    • $ P_x = \lim_{T \Rightarrow \infty}\frac{1}{2T}\int_{-T}^{T} |x(t)|^2\,dt $ for ct (continuous time)

      $ P_x = \lim_{N \Rightarrow \infty}\sum_{n=-N}^{N} |x(n)|^2 $ for dt (discrete time)

      note: for periodic signals
      $ P_x = \frac{1}{N}\sum_{n=0}^{N-1}|x(n)|^2 $

  • Signal RMS (root-mean-square)
    • $ X_{rms} = \sqrt{P_x} $
  • Signal Magnitude
    • $ m_x = max|x(t)| $, for CT

      $ m_x = max|x(n)| $, for DT

      if $ m_x < \infty $, we say signal is bounded


  • Back to ECE

    Back to ECE 301

    Back to ECE 438

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang