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
