Fourier transformation (was: Homework title)

In summary, the problem is to find the Fourier transform of a given function and graph it using the equation F(k) = e^-b|k|. The goal is to show that the resulting function g(x) is equal to (b/pi) × (1/(x^2+b^2)). The person asking for help has already attempted to solve the problem but ran into difficulty.
  • #1
CBuphyx
2
0
Summary: Homework Statement: Fourier

Transform momentum space to normAl space

Homework Equations: F(k)=e^-b|k| show that g(x)=(b/pi)×(1/(x^2+b^2)Hello,I need to that given function Fouirier transform and function of graphic. Thank you😃

Homework Statement: Fourier

Transform momentum space to normAl space

Homework Equations: F(k)=e^-b|k| show that g(x)=(b/pi)×(1/(x^2+b^2)Hello,I need to that given function Fouirier transform and function of graphic. Thank you😃
 
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  • #2
I moved the thread to our homework section and gave it a more descriptive title. Did you plug the function into the Fourier transformation and see what you get? Where did you run into trouble?
 
  • #3
Ok thank you so much
 

1. What is Fourier transformation and why is it important in science?

Fourier transformation is a mathematical technique used to break down a complex signal or function into its individual frequency components. It is important in science because it allows us to analyze and understand complex signals and patterns in a more simplified manner.

2. What are the applications of Fourier transformation?

Fourier transformation has a wide range of applications in various fields such as signal processing, image and sound analysis, data compression, and solving differential equations in physics and engineering.

3. How does Fourier transformation differ from Fourier series?

Fourier transformation is used for continuous and non-periodic signals, while Fourier series is used for periodic signals. Fourier transformation also provides a continuous frequency spectrum, while Fourier series provides a discrete frequency spectrum.

4. Can Fourier transformation be performed on any signal or function?

Yes, Fourier transformation can be applied to any signal or function, as long as it is well-behaved and has a finite integral. However, the results may not always be meaningful or useful depending on the characteristics of the signal.

5. Are there any limitations or challenges when using Fourier transformation?

One limitation of Fourier transformation is that it assumes the signal is stationary, meaning that its characteristics do not change over time. In reality, many signals are non-stationary, which can lead to errors in the analysis. Additionally, the presence of noise in the signal can also affect the accuracy of the results.

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