Re: nyquist freq.
only to illuminate there it is the statement, as our friend echo47 had already exposed.
The Nyquist-Shannon sampling theorem is the fundamental theorem in the field of information theory, in particular telecommunications. It is also known as the Whittaker-Nyquist-Kotelnikov-Shannon sampling theorem or just simply the sampling theorem.
The theorem states that:
when sampling a signal (e.g., converting from an analog signal to digital), the sampling frequency must be greater than twice the bandwidth of the input signal in order to be able to reconstruct the original perfectly from the sampled version.
If B is the bandwidth and Fs is the sampling rate, then the theorem can be stated mathematically (called the "sampling condition" from here on)
2B < Fs
IMPORTANT NOTE: This theorem is commonly misstated/misunderstood (or even mistaught). The sampling rate must be greater than twice the signal bandwidth, not the maximum/highest frequency. A signal is a baseband signal if the maximum/highest frequency coincides with the bandwidth, which means the signal contains zero hertz. Not all signals are baseband signals (e.g., FM radio). This principle finds practical application in the "IF-sampling" techniques used in some digital receivers.