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Fourier Series (16 Videos)

Mathematics : - ( Fourier series ; Introduction ; Periodic function ) - 1.
A Fourier series is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series.[2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood.

Mathematics : - ( Fourier series ; Fourier coefficients ) - 2.
A Fourier series is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series.[2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood.

Mathematics : - ( Conditions for Fourier expansion ) - 3.
Fourier series in general tends to converge slowly. In order for a function f ( x ) to be expanded properly, it must satisfy the following Dirichlet conditions: A piecewise function f ( x ) must be periodic with at most a finite number of discontinuities, and/or a finite number of minima or maxima within one period. Featured playlist

Mathematics : - ( Fourier coefficients when f(x) is odd or even ) - 4.
A function is called even if f(?x)=f(x), e.g. cos(x). A function is called odd if f(?x)=?f(x), e.g. sin(x). These have somewhat different properties than the even and odd numbers: The sum of two even functions is even, and of two odd ones odd.

Mathematics : - ( Fourier series ; Periodic function ) - 5.
A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier Series makes use of the orthogonality relationships of the sine and cosine functions.

Mathematics : - ( Fourier series; Periodic functions ; Solving problem ) - 6.
A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier Series makes use of the orthogonality relationships of the sine and cosine functions.

Mathematics : - ( Fourier series ; Fourier coefficients ) - 7.
A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier Series makes use of the orthogonality relationships of the sine and cosine functions.

Fourier series : - ( Finding Fourier series for the given function ) - 8.
A Fourier series is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series.[2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood.

Mathematics : - ( Fourier Series; Expansion ; Solving problems ) - 9.
A Fourier series is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series.[2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood.

Fourier Series : - ( Fourier expansion of a function ) - 11.
Most of the phenomena that are studied in Engineering and Science are periodic in nature. For instance, current and voltage in an alternating current circuit. These periodic functions could be analysed into their constituent components (fundamentals and harmonics). It can be done by using a process called Fourier analysis.

Fourier series : - ( Harmonic analysis ) - 12.
Harmonic Analysis : The process of finding the Fourier series for a function given by numerical values is known as harmonic analysis. In (1), the term (a1cosx + b1 sinx) is called the fundamental or first harmonic, the term (a2cos2x + b2sin2x) is called the second harmonic and so on.

Fourier Transform : - ( Introduction ) - 13.
In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency.

Fourier transform : - ( Sine and Cosine function ) - 14.
In mathematics, the Fourier sine and cosine transforms are forms of the Fourier transform that do not use complex numbers or require negative frequency. They are the forms originally used by Joseph Fourier and are still preferred in some applications, such as signal processing or statistics.

Fourier transform : - ( Solving problems ) - 15.
In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency.

Fourier Transform : - ( Solving problems ) - 16.
In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency.

Fourier Transform : - ( Solving problem ) - 17.
In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency.

Fourier Series (16 Videos)

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