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science physics# What is the application of Fourier series?

Last Updated: 25th February, 2020

**Fourier series**has manysuch

**applications**in electrical engineering, vibrationanalysis,acoustics, optics, signal processing, image processing,quantummechanics, econometrics, thin-walled shelltheory,etc.

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Accordingly, what is Fourier series and its applications?

**Fourier series** mathematically definesuchwaveforms as functions of displacement (usually amplitude,frequency , or phase ) versus time . As **the** numberofcalculated terms in a **Fourier series** increases,**theseries** more and more closely approximates **the**exactfunction that defines a complex signal waveform.

Likewise, what is the application of Fourier series in engineering? **Fourier Series** are used in the resolutionofPartial Differential Equations, which appears in manyMechanical**Engineering** problems such as Heat Diffusion,WavePropagation and Fluid Mechanics problems. Also, the**FourierTransform**, which is very related to the **FourierSeries**,is used in the Spectrum Analysis ofsignals.

Beside this, what is the use of the Fourier series?

A **Fourier series** is an **expansion** ofaperiodic function in terms of an infinite sum of sines andcosines.**Fourier series** make **use** of theorthogonalityrelationships of the sine and cosinefunctions.

What are the applications of Fast Fourier Transform?

The **FFT**has lotsof **applications** and is used extensively in audioprocessing,radar, sonar and software defined radio to name butafew.