Nyquist Theorem

this theorem defines the "Absolute Theoretical Limit" we can achieve on data transmission speeds error free, over a noiseless communication medium.

Formulated by Harry Nyquist in 1928, it answered a critical engineering question: If a physical channel has a fixed frequency bandwidth, how fast can we toggle signals through it without them smearing into each other?

Theorem

If the highest frequency that the medium can transmit is $f$ then a receiver is able to completely reconstruct the signal by sampling it at $2\cdot f$ (if the channel is noiseless).

$$C = 2B \log_2(M)$$

• C: Maximum data rate (capacity) in bits per second (bps).
• B: Bandwidth of the channel in Hertz (Hz).
• M (or L): Number of discrete signal levels or voltage states used to represent data.

when the medium has noise, Shannon-Hartley Theorem is used.