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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 {\bf 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 {\bf Z}$ (integers)
  • $ t,t_n \in {\bf R}$ (time is always real)

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