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caduceus
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I couldn't understand that why the Fourier integral is meaningless for f(x)=A*cos(ax) ?
Any comments will be appreciated.
Any comments will be appreciated.
caduceus said:I couldn't understand that why the Fourier integral is meaningless for f(x)=A*cos(ax) ?
Any comments will be appreciated.
The Fourier integral gives two delta functions. That is good enough for physicists.caduceus said:I couldn't understand that why the Fourier integral is meaningless for f(x)=A*cos(ax) ?
Any comments will be appreciated.
The Fourier integral is a mathematical tool used to represent any periodic function as a combination of sine and cosine functions. However, for a function like f(x)=A*cos(ax), which is already a cosine function, the Fourier integral becomes meaningless as it is essentially trying to represent the function as a combination of itself.
Yes, the Fourier integral can be used for any periodic function as it breaks down the function into its individual frequency components. However, for functions that are already in the form of a single frequency component, like f(x)=A*cos(ax), the Fourier integral is not necessary.
The Fourier integral is an important mathematical tool that allows us to decompose complex functions into simpler components, making it easier to analyze and understand them. It has applications in various fields such as signal processing, image reconstruction, and quantum mechanics.
Yes, the Fourier integral is also meaningless for functions that are not periodic, as it relies on the periodicity of the function to break it down into frequency components. It is also not applicable for functions that do not have a finite energy, such as the Dirac delta function.
Yes, for functions that are already in the form of a single frequency component, we can use a simpler tool called the Fourier series. This involves representing the function as a sum of harmonically related sine and cosine functions, rather than integrating it over all frequencies as in the Fourier integral.