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)
• $f_s =$ sampling rate, $f_s=\frac{1}{T}$
• $t_n = nT$ (discrete time)
• $n,k \in \mathbb{Z}$ (integers)
• $t,t_n \in \mathbb{R}$ (time is always real)