## Question:

I am currently evaluating the power spectra of a number of process signals. How do I identify the Nyquist frequency with Discrete Fourier Transform (DFT)?

## Answer:

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 follows: $\frac{1}{N \times \frac{1}{F_s}} = \frac{F_s}{N}$.

To recover the original (uncorrupted) signal, first we need $\frac{N}{2}$ (or $\frac{N}{2}+1$, if $N$ is an 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: $\frac{N}{2} \times \frac{F_s}{N} = \frac{F_s}{2}$

## Comments

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

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

Let's walk through the rationale:

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

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