How to Achieve Zero-Bandwidth Modulation

April 08, 2020 //By A Delapalisse
How to Achieve Zero-Bandwidth Modulation
Perhaps Shannon and Hartley were wrong after all? Let’s look at the math. (In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise)

The curse of the communications engineer has always been getting maximum data rate through the narrowest channel. In broadband applications, modulation provides the carrier, but in all cases, the resulting sidebands eat up the bandwidth. Now a recent discovery lets you achieve your data objective with zero bandwidth modulation.


Hidden from discovery in plain view for decades, this method has some engineers wondering if all that they ever knew about spectral efficiency is wrong. ( see the Shannon–Hartley theorem )  You can prove this recent discovery by going through the math yourself. All you really need to remember are some basic trigonometric identities:

  • sin A sin B = 0.5[cos (A B) cos (A + B)]
  • cos A cos B = 0.5[cos (A B) + cos (A + B)]
  • sin A cos B = 0.5[sin (A B) + sin (A + B)]

Write the math through the modulation circuit in the figure and voilà

The zero-bandwidth modulator.                                                                       

Let's do the maths

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