Notation

Frequency and Time:

$\omega$ denotes continuous radian frequency (rad/sec)

$f$ denotes continuous frequency in Hertz (Hz)

$\omega= 2\pi f$

$\omega_k$ denotes discrete frequency, $\omega_k = 2\pi (k/N) f_s$

$\omega, \omega_k \in \mathbb{R}$ (frequencies are always real)

$T =$ sampling interval (sec) (typically $T=1$ )

$f_s =$ sampling rate, $f_s=\frac{1}{T}$

$t_n = nT$ (discrete time)

$n,k \in \mathbb{Z}$ (integers)

$t,t_n \in \mathbb{R}$ (times are always real)