# How to identify the Nyquist frequency with DFT

I am currently evaluating the power spectra of a number of process signals. How do I identify the Nyquist frequencies of the various components?

• The Nyquist frequency is one half (0.5) of the data set sampling frequency.

http://paulbourke.net/miscellaneous/dft/

Let's walk through the rationale:

• Let $F_s$ be the sampling rate (frequency) of the observations in the data set.
• Let $N$ be the number of observations in our data set.
• Let $T$ be the time duration span in the data set.
• The fundamental frequency of DFT is defined as $\frac{1}{T}$.
• Alternatively, the fundamental frequency can be expressed as follow: $\frac{1}{N * \frac{1}{F_s}} = \frac{F_s}{N}$.
• To recover the original (uncorrupted) signal, we need 1st $\frac{N}{2}$ ($N$ is even number) or $\frac{N}{2}+1$ ($N$ is odd number) frequency components, as the DFT spectrum is symmetrical around such frequency.

Therefore, the frequency of the $\frac{N}{2}$ (or $\frac{N}{2}+1$) DFT component is equal to the Nyquist frequency, which is: $\frac{N}{2}* \frac{F_s}{N} = \frac{F_s}{2}$