On 26th January we celebrated the 90th anniversary of the 1st demonstration of television and I thought it would be a good idea to search something about the mathematics behind the whole technology. So, I thought I should be faithful to my motto: “The study of mathematics is like air or water to our technological society.” and make a small post on the mathematics behind this technology. I have to admit that I am by far no specialist in this and if there are any mistakes in my understanding just feel free to let me know in the comment box bellow.

Using the old trusty Wikipedia, which just celebrated 15 years of existence, I had a look at the components of a TV and a small inside into what exactly is happening in there. Starting with something more easy: pixel resolution. This refers to the number of pixels in an image. Resolution is sometimes identified by the width and height of the image as well as the total number of pixels in the image. For this was easy to identify the mathematics behind it, it is just basic rectangle area and counting pixels. So nothing fancy in here so far. Going gradually to harder things we have the contrast ratio, which is the measurement of the range between the lightest and darkest points on the screen, and the aspect ratio, the ratio of horizontal to vertical measurements of a television picture. For these last things we have just proportion or ratio, nothing out of ordinary.

The things are escalating a little fast when we get to image and sound source. Both of these use electrical signal: for image source we have video camera (live television), video tape recorder (recorded images) and telecine with a flying spot scanner (transfer of motion picture to video); for sound source we have microphone and audio output of a video tape recorder. Now, when we get to electrical signal there is electrical engineering and I believe that some of you already know that you need linear algebra and differential equations to get a chance to understand this topic. Moreover, we have some modelling mathematics hidden in here, too. Modelling mathematics has updated to dynamical systems tools including differential equations, and more recently, Lagrangians. Obviously here is a combination of mathematics and physics and it is hard to say exactly where one starts and the other ends.

Going deeper into the problem we have a transmitter (radio signals into radio waves), television antenna ( receive and broadcast the encoded signals), receiver (decodes the picture and sound information from the broadcast signals), display device (turns electrical signal into visual image) and audio amplifier/loudspeaker (turns electrical signals into sound waves). Firstly, taking a look at radio signals we get into the mathematics of radio engineering which is based on complex analysis. Secondly, radio waves takes us to the mathematical theory behind waves, which starts with the basic sine and cosine functions (trigonometry at its maximum) and end with differential equations. Lastly, we get to the encoded/decoded signals which have to do with old cryptology we all love from old times. This time we have a combination of mathematics, physics and computer science, they seem to always work well together.

To conclude this article, maybe I should say something about the mathematics involved into signal science in general. It is a complicated topic and involves some high mathematics like Laplace and Fourier transformations, Lagrangians, probability and differential equations. With this I end the list of mathematical topics behind the television technology. I have never done something like this before, but let me know if you would like to see more posts like this one.

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Don’t forget that maths is everywhere! Enjoy! ~LThMath~