(New page: So many symbols, so little time... Here's a quick lookup table for our commonly-used symbols! *<math>\omega_s</math>: Sampling frequency; equal to <math>\frac{2\pi}{T}</math> *<math>\omega...) |
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| − | So many symbols, so little time... Here's a quick lookup table for our commonly-used symbols! | + | So many symbols, so little time... Here's a quick lookup table for our commonly-used symbols! |
*<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>s</math>: A complex number -- often expressed as a sum of it's parts, <math>a+j\omega</math>, where <math>a, \omega \in \mathbb{R}</math> | *<math>s</math>: A complex number -- often expressed as a sum of it's parts, <math>a+j\omega</math>, where <math>a, \omega \in \mathbb{R}</math> | ||
*<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 | ||
Revision as of 14:31, 27 January 2009
So many symbols, so little time... Here's a quick lookup table for our commonly-used symbols!
- $ \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
