You will find that a square wave can be made from an infinite number of odd harmonic sine waves of progressively reducing amplitude. So, for a Hz square wave, you would need to add together a Hz sine wave as well as Hz, Hz, Hz etc. You need an infinite number of harmonics to produce a perfect square wave and quite a lot of harmonics to get close to a square wave. The example above shows what happens if you start with Hz sine wave red trace then add in the right proportion of Hz green trace , then add Hz as well blue trace and finally Hz cyan trace.
While the waveform is now looking a lot less like a sine wave it is a long way from a perfect square wave. Even with 32 frequencies i. However, this is a mathematical exercise. Notify me of new posts by email. There's a book! It's a collection of over fifty of my favorite articles, revised and updated.
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Home About Faq. Do they exist in nature? Q: Why are the days still longer than nights, until a few days after the fall equinox?
Q: What is a Fourier transform? What is it used for? Posted on September 24, by The Physicist. Email Print Facebook Reddit Twitter. This entry was posted in -- By the Physicist , Equations , Math. Bookmark the permalink. Lucas says:. September 25, at am. Bear says:.
September 25, at pm. Good stuff, Physicist. Thank you. Jose E Castro E says:. April 30, at pm. June 4, at pm. July 28, at am. Shiva Rama Krishna says:. August 18, at am. Shahrier says:. January 19, at am. March 13, at am.
Kirti Batish says:. April 8, at pm. June 25, at am. August 23, at am. November 5, at pm. December 10, at am. The Physicist says:. Most of the phenomena studied in the domain of Engineering and Science are periodic in nature. For instance, current and voltage in an alternating current circuit. These periodic functions could be analyzed into their constituent components fundamentals and harmonics by a process known as Fourier analysis. Periodic functions occur frequently in the problems studied through engineering education.
Their representation in terms of simple periodic functions such as sine function and cosine function, which leads to Fourier series FS. The Fourier series is known to be a very powerful tool in connection with various problems involving partial differential equations. In this article,we will discuss the Fourier analysis with fourier series examples and fourier series notes.
This application is important not only for practical reasons PDEs are important for physics obviously , but it also has particular historical relevance as it is apparently what initially motivated Fourier, so we can imagine that it will be simple and intuitive. Trying a solution of this form is just a guess, and initially we have no reason to be sure it will work out.
These are just simple ordinary differential equations that we know how to solve! Given the boundary conditions, the solutions are:. We could then plug those back in the equation to confirm that our separation of variables guess does give possible answers.
Because the equation is linear, multiplying a solution by a constant or adding two solutions together is another solution, so we reach a general solution form of:. If we couldn't, then this approach wouldn't be very useful!
But luckily the answer is yes for a very wide class of functions that satisfies most of our needs. Previously, we discussed the heat equation. But separation of variables and the Fourier transform can be used solve other very important PDEs as well, which makes this method even more important. In that case, due to the second time derivative, we have two functions for the initial condition: position and speed of each point. And it turns out that for the solution we have to take the Fourier transform of each separately.
Schrodinger equation in cartesian coordinates: analogous to the heat equation, since we have a time derivative of order 1. For example, for a quantum free particle , the solution is a sum of complex exponentials. We radio hams have developed new modes of digital communication that use discrete Fourier transforms to extract signals that are so deeply buried in noise that the human ear would not notice them. This allows communication with very low power at reduced speed, of course.
This is similar to what the SETI program does in its search for bug eyed monster civilizations in outer space. So far they haven't admitted to finding anything. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Real world application of Fourier series Ask Question. Asked 7 years, 11 months ago.
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