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When we do a Fourier transformation of a function we get the primary term which is the fundamental frequency and amplitude of the Fourier series. All the other terms, with higher frequencies and lower amplitudes, are the harmonics.
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In Fourier transformation and Fourier series which one follows periodic nature?
The Fourier series can be used to represent any periodic signal using a summation of sines and cosines of different frequencies and amplitudes. Since sines and cosines are periodic, they must form another periodic signal. Thus, the Fourier series is period in nature. The Fourier series is expanded then, to the complex plane, and can be applied to non-periodic signals. This gave rise to the Fourier transform, which represents a signal in the frequency-domain. See links.
Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
Fourier series of sine wave?
The fourier series of a sine wave is 100% fundamental, 0% any harmonics.
Is Fourier series used in power electronics to generate harmonics?
Yes, Fourier series can be used in power electronics to analyze and generate harmonics. By decomposing complex waveforms into their sinusoidal components, engineers can understand and manipulate the harmonic content of signals. This is particularly useful in applications like pulse-width modulation (PWM) for inverters, where controlling harmonics is essential for improving power quality and efficiency. Additionally, Fourier analysis helps in designing filters to mitigate unwanted harmonics in power systems.
What is fourier series?
Consider a periodic function, generally defined by f(x+t) = f(x) for some t. Any periodic function can be written as an infinite sum of sines and cosines. This is called a Fourier series.
In Mathematics what is meant by the Fourier series?
The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
In Fourier transformation and Fourier series which one follows periodic nature?
The Fourier series can be used to represent any periodic signal using a summation of sines and cosines of different frequencies and amplitudes. Since sines and cosines are periodic, they must form another periodic signal. Thus, the Fourier series is period in nature. The Fourier series is expanded then, to the complex plane, and can be applied to non-periodic signals. This gave rise to the Fourier transform, which represents a signal in the frequency-domain. See links.
What are Joseph Fourier's works?
Fourier series and the Fourier transform
What are the limitation of fourier series?
what are the limitations of forier series over fourier transform
Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
What is the physical significance of fourier series?
The Fourier series is important because it allows one to model periodic signals as a sum of distinct harmonic components. In other words, representing signals in this way allows one to see the harmonics in a signal distinctly, which makes it easy to see what frequencies the signal contains in order to filter/manipulate particular frequency components.
Can a discontinuous function can be developed in the Fourier series?
Yes. For example: A square wave has a Fourier series.
What is physical significance of Fourier series?
Fourier series is series which help us to solve certain physical equations effectively
What is the difference between fourier series and discrete fourier transform?
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
How do you find the inverse Fourier transform from Fourier series coefficients?
To find the inverse Fourier transform from Fourier series coefficients, you first need to express the Fourier series coefficients in terms of the complex exponential form. Then, you can use the inverse Fourier transform formula, which involves integrating the product of the Fourier series coefficients and the complex exponential function with respect to the frequency variable. This process allows you to reconstruct the original time-domain signal from its frequency-domain representation.
Fourier series of sine wave?
The fourier series of a sine wave is 100% fundamental, 0% any harmonics.
Why was Joseph Fourier famous?
Joseph Fourier was the French mathematician and physicist after whom Fourier Series, Fourier's Law, and the Fourier Transform were named. He is commonly credited with discovering the greenhouse effect.
