## Smart answer:

# Your search for *′What is a Fourier series′* returned the following results:

### a function represented as an infinite sum of sine and cosine terms

Basically the Fourier Series is a function represented as an infinite sum of sine and cosine terms.

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### a way to represent a function as the sum of simple sine waves

In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.

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### a summation of harmonically related sinusoidal functions, also known as components or harmonics

A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics.

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### a method of expressing a periodic function in terms of sinusoidal basis functions

The Fourier series is a method of expressing a periodic function in terms of sinusoidal basis functions.

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### an expansion of a periodic function f (t)

Signals & Systems R. M. Taufika R. Ismail FKEE, UMP Introduction A Fourier series is an expansion of a periodic function f (t) in terms of an infinite sum of cosines and

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### for periodic functions

The Fourier series is defined for periodic functions, integrating > (or summing) over one period.

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### this method of decomposing periodic functions into sines

Depending on how the original signal is expressed, this method of decomposing periodic functions into sines is known as Fourier series or Fourier transform.

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### a series whose terms are composed of trigonometric functions

A Fourier series is a series whose terms are composed of trigonometric functions.

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### This superposition or linear combination

This superposition or linear combination is called the Fourier series.

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### Weierstrass function (originally defined as a Fourier series)

Weierstrass function (originally defined as a Fourier series) was the first instance in which the idea that a continuous function must be differentiable was introduced.

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### a way to approximate any arbitrary periodic signal as the sum of sines and cosines

The Fourier Series is a way to approximate any arbitrary periodic signal as the sum of sines and cosines.

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### a way of expressing periodic functions they aren't random

Fourier series are a way of expressing periodic functions they aren't random, they repeat.

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### a mathematical tool used for analyzing periodic functions by decomposing such a function into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short

The Fourier series is a mathematical tool used for analyzing periodic functions by decomposing such a function into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short.

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### an infinite sequence of terms used to solve special types of problems

In mathematics, the Fourier series is an infinite sequence of terms used to solve special types of problems.

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### a sum of this form: where each of the squares () is a different number, and one is adding infinitely many terms.

A Fourier series is a sum of this form: where each of the squares () is a different number, and one is adding infinitely many terms.

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### The inverse transform

The inverse transform, known as Fourier series, is a representation of in terms of a summation of a potentially infinite number of harmonically related sinusoids or complex exponential functions, each with an amplitude and phase specified by one of the coefficients:

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### a series that decomposes any periodic curves into a sum of sines and cosines

The Fourier Series is a series that decomposes any periodic curves into a sum of sines and cosines.

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### a way to represent complex waves, such as sound, as a series of simple sine waves

A Fourier series is a way to represent complex waves, such as sound, as a series of simple sine waves.

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