Shannon-Hartley Theorem

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

Formulated by Claude Shannon in 1948, it is considered the foundational cornerstone of modern information theory and telecommunications.

The Formula

The theorem expresses the maximum channel capacity ($C$) as a function of bandwidth ($B$) and signal-to-noise ratio ($\text{SNR}$):

Variable Breakdown:

• $C$ (Channel Capacity): The maximum achievable data rate in bits per second (bps).
• $B$ (Bandwidth): The frequency range of the channel measured in Hertz (Hz).
• $\text{SNR}$: The ratio of signal power to noise power ($P_{\text{signal}} / P_{\text{noise}}$), expressed as a linear ratio (not in dB). Properties of Periodic Signals#Signal to Noise Ratio (SNR)