Fourier Explained: [3Blue1Brown] Style!

If you ask most people to explain the Fourier series they will tell you how you can decompose any particular wave into a sum of sine waves. We’ve used that explanation before ourselves, and it is not incorrect. In fact, it is how Fourier first worked out his famous series. However, it is only part of the story and master video maker [3Blue1Brown] explains the story in his usual entertaining and informative way. You can see the video below.

Paradoxically, [3Blue1Brown] asserts that it is easier to understand the series by thinking of functions with complex number outputs producing rotating vectors in a two-dimensional space. If you watch the video, you’ll see it is an easier way to work it out and it also lets you draw very cool pictures.

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Wolfram Engine Now Free… Sort Of

You’ve probably used Wolfram Alpha and maybe even used the company’s desktop software for high-powered math such as Mathematica. One of the interesting things about all of Wolfram’s mathematics software is that it shares a common core engine — the Wolfram Engine. As of this month, the company is allowing free use of the engine in software projects. The catch? It is only for preproduction use. If you are going into production you need a license, although a free open source project can apply for a free license. Naturally, Wolfram gets to decide what is production, although the actual license is pretty clear that non-commercial projects for personal use and approved open source projects can continue to use the free license. In addition, work you do for a school or large company may already be covered by a site license.

Given how comprehensive the engine is, this is reasonably generous. The engine even has access to the Wolfram Knowledgebase (with a free Basic subscription). If you don’t want to be connected, though, you don’t have to be. You just won’t be able to get live data. If you want to play with the engine, you can use the Wolfram Cloud Sandbox in which you can try some samples.

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The Kalman Filter Exposed

If we are hiring someone such as a carpenter or an auto mechanic, we always look for two things: what kind of tools they have and what they do when things go wrong. For many types of embedded systems, one important tool that serious developers use is the Kalman filter. It is also something you use when things go “wrong.” [Carcano] recently posted a tutorial on Kalman filter equations that tries to demystify the topic. His example — a case of things going wrong — is when you have a robot that knows how far it is supposed to move and also has GPS coordinates of its positions. Since the positions probably don’t agree, you can consider that a problem with the system.

The obvious answer is to average the two positions. That’s fine if the error is small. But a Kalman filter is much more robust in more situations. [Carcano] does a good job of taking you through the math, but we will warn you it is plenty of math. If you don’t know what a Gaussian distribution is or the word covariance makes you think of sailboats, you are going to have to do some reading to get through the post.

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Understanding Math Rather Than Merely Learning It

There’s a line from the original Star Trek where Khan says, “Improve a mechanical device and you may double productivity, but improve man and you gain a thousandfold.” Joan Horvath and Rich Cameron have the same idea about improving education, particularly autodidacticism or self-learning. They share what they’ve learned about acquiring an intuitive understanding of difficult math at the Hackaday Superconference and you can watch the newly published video below.

The start of this was the pair’s collaboration on a book about 3D printing science projects. Joan has a traditional education from MIT and Rich is a self-taught guy. This gave them a unique perspective from both sides of the street. They started looking at calculus — a subject that scares a lot of people but is really integral (no pun intended) to a lot of serious science and engineering.

You probably know that Newton and Leibniz struck on the fundamentals of calculus about the same time. The original papers, however, were decidedly different. Newton’s approach was more physical and less mathematical. Leibniz used formal logic and algebra. Although both share credit, the Leibniz notation won out and is what we use today.

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An Abstract Kind Of Clock: The Chinese Remainder Clock

Hackaday likes clocks, a lot. Speaking personally, from my desk I can count at least eight clocks, of which seven are working. There’s normal quartz movement analog clocks, fun automatic wristwatches, run-of-the-mill digital clocks, a calculator watch, and a very special and very broken Darth Vader digital clock/radio combo that will get fixed one day — most likely. Every clock is great, and one of life’s great struggles is to see how many you can amass before you die. The more unique the clock is, the better, and nothing (so far) tops [Antonella Perucca]’s Chinese Remainder Clock.

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FxSolver Is A Math Notebook For Engineers

If you like to rely on the web to do your electronics and computer math, you’ll want to bookmark FxSolver. It has a wide collection of formulae from disciplines ranging from electronics, computer science, physics, chemistry, and mechanics. There are also the classic math formulations, too.

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Wolfram Alpha Electronic Tips

Electronics takes a lot of math. Once you’ve mastered all the algebra and calculus, though, it is sometimes a drag to go through the motions. It also can be error-prone. But these days, you have Wolfram Alpha which will do all the work for you and very easily. I use it all the time when I’m too lazy to solve an equation or do an integral by hand. But did you know it actually has some features specifically for electronics?

If you want to do a lot with electronics — or nearly any technical field — you are going to have to learn some math and you shouldn’t just rely on tools like Wolfram to skirt understanding the math. Unfortunately, schools often teach us that the point to math is to get a correct answer. For bookkeepers and at the very final stage of engineering, that may be true. But the real value to math for engineers and scientists is to develop intuition about things. If you increase a capacitor’s value does that make its reactance go up or down? Does a little change in load resistance make a corresponding small change in power consumption or is it a lot more? So you should understand why math works. But once you do, using a tool like Wolfram can free you to focus on the abstract questions instead of the detailed “grunt work.”

 

Tip #1: Split Personality

Wolfram can’t seem to decide if it is a symbolic math program or a search engine. Sometimes just putting a topic name in can lead to some interesting calculations. For example, look what happens when you enter the word opamp: Continue reading “Wolfram Alpha Electronic Tips”