[] What is fourier transform and how is it used in antenna application?

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I am a new radio ham with general license and is trying to dive into antenna theory. As the question suggests, I want to know more about fourier transform. With all the resources I can find on the internet, no one seemed to be able to explain it in layman’s terms without showing shitty formulas that I don’t understand. I would like someone to explain fourier transform with little math as possible, or teach me any math concepts involved.

What is fourier transform? How does it work? How is the formulas derived? What are its appliations in communication antennas?

In: Engineering

3 Answers

Anonymous 0 Comments

In RF and other repeating/periodic signals, you’re not as much interested in each point in time as much as you are the repeating patterns.

Fourier turns Calculus back into Algebra II and looks at frequency instead of time.

Anonymous 0 Comments

Suppose I had some sheet music that specified the some notes and volumes of those notes, and played it on a piano, it would obviously produce a sound. A Fourier Transform essentially does the opposite, it takes a sound, and breaks it down into the notes that make up the sound.

Edit: Sound is made up of waves, and there are a bunch of ways to organize the sound waves, but the simplest way mathematically to do that is based on the frequency, and to plug that frequency into a complex exponential (or a sine and cosine). So if you look at the formula’s for Fourier Transforms, you’ll see those guys cropping up. The derivation of the fourier transform is essentially a generalization of the dot product from early vector math, but instead of seeing how well two vectors line up with each other, you see how well two functions do so.

Anonymous 0 Comments

The Fourier Transform is a mathematical way to take a time-varying waveform and convert it into a set of frequencies.

You can take almost any periodic (repeating) signal and recreate it or closely approximate it by adding up a bunch of sine waves (or cosine waves) of different amplitudes and phases. The Fourier Transform is the math to figure out what those are. So we say that the FT converts a signal from the “time domain” to the “frequency domain”. It’s kind of like what a frequency analyzer does, if you are familiar with those.

And even most non-periodic signals can also have the FT applied, but the combination of sine waves used may also need to change over time.

In antenna theory, the FT can be used to help do the math to figure out the antenna radiation pattern as a function of the angle with respect to the antenna. But it’s a lot of math, and not really that necessary for a beginner or general ham user.

If you are really determined to learn how this works, you’re going to want to learn calculus. I can’t teach you that in a reddit post.