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Tech2025
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Working on some microwave stuff, read about this but can't understand the explanations online.
What are Fourier Series in layman's terms ?sophiecentaur said:What's the question?
Basically what I understand is that it is a method to find different parts of a continuous signal.sophiecentaur said:What have you found out and read so far?
Thank you! Finally something that made sensesophiecentaur said:Hmm. The Fourier Transform transforms a signal in the time domain (a varying voltage or whatever) into the frequency domain (a set of frequencies). It strictly applies to an infinitely long signal (with no beginning or end) and the resulting frequency domain signal can consist of a continuum of values.
Engineers use a Discrete Fourier Transform and that assumes a repeating g signal which you represent by a fixed number of values in a time window - say a sampled waveform from an electronic organ note. The DFT gives you a set of values of frequencies in that signal and the frequencies are all harmonics of the fundamental note. At its simplest, it would correspond to the draw-bar settings on an old fashioned Hammond Organ which give a particular audio wave form.
The Fast Fourier Transform is just a smart way to speed up the Fourier analysis by always using a number of samples that is a power of 2. i.e. 256 samples or 2048 or as many as you lime, depending on the accuracy you want. Single chips are available that will do that for you.
Glad that taster helped. There is a lot more to it, remember.Tech2025 said:Thank you! Finally something that made sense
A Fourier series is a mathematical representation of a periodic function as a sum of sinusoidal functions. It is named after the French mathematician Joseph Fourier and is widely used in many fields, including physics, engineering, and signal processing.
A Fourier series works by breaking down a periodic function into an infinite sum of sine and cosine functions with different amplitudes and frequencies. This allows us to represent the original function in terms of simpler components, making it easier to analyze and manipulate.
A Fourier series is useful because it allows us to represent complex periodic functions in terms of simpler components, making it easier to analyze and manipulate them. It also has applications in fields such as signal processing, where it is used to analyze and filter signals.
Some common applications of Fourier series include audio and image compression, signal analysis and filtering, solving differential equations, and solving boundary value problems in physics and engineering.
Yes, there are some limitations to Fourier series. It is only applicable to periodic functions, which means it cannot be used to represent non-periodic functions. It also assumes that the function is continuous and has a finite number of discontinuities. In some cases, it may also require an infinite number of terms to accurately represent a function.