(Brian Thomas, Rhea HW9 (part 1)) |
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*<math>p(t)</math>: "Impulse train" -- equivalent to <math>\sum_{n=-\infty}^{\infty} \delta(t-nT)</math> | *<math>p(t)</math>: "Impulse train" -- equivalent to <math>\sum_{n=-\infty}^{\infty} \delta(t-nT)</math> | ||
| − | ==Chapter | + | ==Chapter 9: Laplace Transforms== |
*<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>. | ||
Latest revision as of 18:31, 23 November 2008
So many symbols, so little time... Here's a quick lookup table for our commonly-used symbols!
Chapter 7
- $ \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) $
Chapter 9: Laplace Transforms
- $ 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) $.
