Inverse Fourier Tranform of Transmission Lines Wave Equation

In summary, the conversation discusses the process of solving a PDE using Fourier transforms. The person is struggling with understanding the inverse Fourier transform of e^(-jwx/u) and is using Laplace transforms to perform Fourier transformations. They are advised to clearly define the problem and write it out carefully.
  • #1
NZBRU
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Homework Statement


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From the derivation of v(x,t) and i(x,t) I am stuck on how the inverse Fourier transform of e^(-jwx/u) was calculated. I am trying to understand how the PDE was fully solved here: http://fourier.eng.hmc.edu/e84/lectures/transmission_line/node1.html

Homework Equations


Not sure what rule to implement here, working using laplace transforms (s = jw) to perform Fourier transformations to avoid integration.
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The Attempt at a Solution


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  • #2
Your notation and writing are a mess. You have f as a function of x in some places, of t in other places, and x and t in yet other places. Why don't you start by clearly defining what the problem is and writing it out carefully.
 
  • #3
And type it instead of posting an image.
 

FAQ: Inverse Fourier Tranform of Transmission Lines Wave Equation

1. What is the inverse Fourier transform of a transmission line wave equation?

The inverse Fourier transform of a transmission line wave equation is a mathematical operation used to convert a signal from the frequency domain to the time domain. It is also known as a time-domain reflection coefficient and is used to analyze the behavior of electromagnetic waves in transmission lines.

2. How is the inverse Fourier transform of a transmission line wave equation calculated?

The inverse Fourier transform of a transmission line wave equation is calculated using the Fourier transform equation, which involves integrating the product of the signal and a complex exponential function over all frequencies. This calculation can be done using various mathematical techniques such as integration by parts or the Cauchy residue theorem.

3. What is the significance of the inverse Fourier transform in transmission line analysis?

The inverse Fourier transform plays a crucial role in the analysis of transmission lines as it allows for the conversion of a signal from the frequency domain to the time domain. This helps in understanding the behavior of electromagnetic waves and their interactions with the transmission line components, such as resistors and capacitors.

4. How is the inverse Fourier transform related to the forward Fourier transform?

The inverse Fourier transform and the forward Fourier transform are inversely related to each other. This means that applying the inverse Fourier transform to a signal that has been transformed using the forward Fourier transform will result in the original signal being recovered.

5. What are some applications of the inverse Fourier transform of a transmission line wave equation?

The inverse Fourier transform of a transmission line wave equation has various applications in the field of electrical engineering, particularly in the analysis and design of transmission lines. It is also used in signal processing, data compression, and communications systems for converting signals from the frequency domain to the time domain for easier analysis and interpretation.

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