How are radio waves mathematically expressed?

Question

Hello! I’m trying to educate myself on radio transmissions. I started with [Basics for dummies](https://www.dummies.com/article/technology/digital-audio-radio/ham-radio/basics-of-radio-waves-160691/)

That article describes radio waves as frequency and wavelength. The [1977 Wow! Signal](https://en.wikipedia.org/wiki/Wow!_signal) is expressed in frequency and bandwidth.

Can someone help elucidate the difference for me?

And how is this mathematically expressed? Would a radio wave be expressed as a “1420 Mhz wavelength signalin the 10 kHz band?” Something else?

Thanks!

In: Mathematics

Answer 1

It depends on who you’re communicating to and what radio waves you’re talking about.

Any waveform can be represented as a sum of sine waves of varying frequencies. Frequency and wavelength are directly related as the inverse of each other. If you record some radio transmission and apply a Fourier transform to it, what you’ll see is a “spectrum” showing how much of each sine wave exists in the signal. You can measure this through an instrument called a [spectrum analyzer](https://en.wikipedia.org/wiki/Spectrum_analyzer?wprov=sfti1). A sine wave is expressed as A x sin(2 x pi x f + phi), where “A” is its amplitude (how big it is), “f” is its frequency (how fast the sin cycles), and “phi” is its phase (sin(0) is 0. A phase would offset that).

A signals bandwidth typically refers to how “wide” the signal is on the spectrum. Frequency may generally refer to the center of the band. Something like an FM transmission would be described as an FM transmission on channel 103.3. “Channel” represents a center frequency of 103.3 MHz and FM channels have standardized bandwidths of 0.2 MHz, which means a particular FM transmission on that channel can have frequency content between 103.2 and 103.4 MHz.

When a signal is transmitted, a “carrier wave” is first generated. In the case above, that would be 103.3 MHz, or A x sin(2 x pi x (103.3MHz) + phi) It would then be “modulated” with the data to be transmitted, which in the case of an FM radio station is music or a host’s voice. This mathematically is represented by multiplying the data with the carrier wave. Practically, what this does is moves the 0.2 MHz-wide data into the 103.3 MHz channel from “baseband”.