Fourier Transform Of Coulomb Potential Fourier Transform Of Coulomb Potential In mathematics, Fourier transform consider as an operation that has various application in engineering, physics or other related field that define a mathematical function of time as a frequency with function, which is known as frequency spectrum. The theorems of Fourier transform always fulfill this process to be done. In the Fourier transform the function with time variable are known as time-domain representation. So, we can say that function of frequency spectrum known as frequency domain representation. In the simple definition of Fourier transform, it can be referred as the transform operation and complex valued function that it produces. Fourier series was developed by the famous mathematician Jean Baptiste Fourier. He specify that any type of Imaginary periodic function can be written as a sum of sine and the cosine functions. The Fourier transformation can be performed by the calculation of discrete set of complex amplitude, which is known as Fourier series coefficient.
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The basic operation of the Fourier transform is based on a Fourier series. In the Fourier series mathematical functions can be define as a sum of the mathematical waves represented by the sine and cosine values. So, we can sat that Fourier transform describe the relation between two things that is a signal in time domain and the representation of the frequency domain. When we perform the Fourier transform then they have no effect on the initial information. It means that no information is created or lost during the transformation process, through this ability we can recovered the original signal from knowing the Fourier transform and vice versa. Fourier transform of a signal, is the continues value that capable of representing real valued or complex valued continues time signals. The Fourier transform can simply be defined by the equation: x (f) = ∫-∞∞ x(t) e-y2pi f t dt In the above given equation x (f) is the representation of Fourier transform of x(t). This Frequency is measured in Hz with f as the frequency variables. In this session we show you the process of solving the wave and telegraph equations on the full real line by transforming. The transformation can be performed by using the Fourier series. To solve the Fourier Transform Equation we need the knowledge of properties of the Fourier Transform. Suppose that x ( e ), y ( e ) and z ( e ) are the integer able function, which can be written as: ∫-∞∞ x(a) dx < ∞. The above equation can be used in various type of Fourier transformation properties:
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Linearity: According to this properties any complex number a and b, if h( e) = ax(e) + by(e), then h’(e) = a . x’ (e) + b .y’(e). Translation: According to this properties for any type of real number a0, if h ( a ) = f (a – a0) then h’(e) = e-2 ∏ I a0 e f’(e) Modulation: According to this property for any real number e0, if in case h(a) = e2 ∏ I a0 e f(a), then h’(e) = f’(e – e0). Scaling: according to scaling property of Fourier Transformation for any non zero real number a, if h(a) = f (ea) then h’(a) = 1 / a f’ ( e / f(e).
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