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Studious_stud
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Homework Statement
The Attempt at a Solution
When I do the integral of this function I'm unsure of what the limits are. Anyone care to help? Thanks
What are the limits of a Fourier integral?
In summary, the conversation is about finding the limits for an integral of a given function, with one person initially unsure of the limits and asking for help. Another person provides a solution using latex, but then another person confirms that the lower limit is 0 and the upper limit is infinity. The conversation ends with a clarification on the upper limit.
When I do the integral of this function I'm unsure of what the limits are. Anyone care to help? Thanks
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Please include an attempt or this thread will be deleted.
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Studious_stud
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micromass said:
Sure thing, just forgot to include it.
I'd use latex but it's just quicker this way...
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Well f(x)=0 for [itex]x\leq 0[/itex], so the part of the integral from [itex]-\infty[/itex] to 0 vanishes, right??
So that would leave us with?
So that would leave us with?
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Studious_stud
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micromass said:
Oh I get ya, so the lower limit is 0 and the upper limit is [itex]-\infty[/itex]?
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Studious_stud said:
I guess you mean + for the upper limit, but yeah.
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Studious_stud
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Studious_stud said:
Sorry for the double post here, I mean the upper limit is [itex]\infty[/itex]
FAQ: What are the limits of a Fourier integral?
What is a Fourier Integral?
A Fourier Integral is a mathematical tool used to decompose a complex function into its individual frequency components. It helps in understanding the behavior of a function in terms of its frequency components.
What are the uses of Fourier Integrals?
Fourier Integrals have a wide range of applications in various fields such as signal processing, engineering, physics, and mathematics. They are used to analyze and interpret complex signals and functions, and also to solve differential equations.
What are the limitations of Fourier Integrals?
One of the main limitations of Fourier Integrals is that they assume the function to be a continuous and periodic signal. This may not always be the case in real-world applications, leading to inaccuracies in the analysis.
Additionally, Fourier Integrals cannot handle functions with discontinuities or singularities, as they require the function to be differentiable at every point.
What is the difference between Fourier Integrals and Fourier Series?
Fourier Integrals and Fourier Series are both mathematical tools used to analyze functions in terms of their frequency components. The main difference is that Fourier Series is used for periodic functions, while Fourier Integrals can be applied to non-periodic functions.
What are some common techniques to overcome the limitations of Fourier Integrals?
Some common techniques used to overcome the limitations of Fourier Integrals include windowing, which involves multiplying the function with a window function to make it periodic, and using different types of Fourier Transforms such as the Discrete Fourier Transform or the Fast Fourier Transform.
Other techniques include using advanced mathematical methods such as the Laplace Transform or the Wavelet Transform, which can handle functions with discontinuities and singularities.