Correctness of Equations in Electromagnetism Textbook

In summary, the conversation revolves around a set of equations that were sourced from a Russian handbook for electricians. The speaker is unsure if the equations are mathematically correct and is seeking a simple YES/NO answer. They also mention that the equations involve Fourier's inverse transform applied in electromagnetism and have been copied from the textbook, but may contain errors due to notation. The conversation ends with a request for the name and specific location of the equations in the source.
  • #1
DesertFox
Hello buddies!
Please, check out these equations...
Tell me, please, are they mathematically correct or not?

I need a simple YES/NO answer.
I have not sufficient knowledge to understand them. I just need to know whether they are correct...

Thank you!

P.S. Am is amplitude; I guess it is a form of Fourier's inverse transform applied in electromagnetism...

CodeCogsEqn (7).gif
 
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  • #2
What is the source of these equations?
 
  • #3
Dale said:
What is the source of these equations?
A russian handbook for electricians..
 
  • #4
Is it this same book that we have discussed here previously?
 
  • #5
Dale said:
Is it this same book that we have discussed here previously?
No. This one is from Russian source! Is it correct?
 
  • Like
Likes Dale
  • #6
After the third equal sign the expression loses its dependence on t, so that seems wrong. The infinity/-infinity is not terribly meaningful either.
 
  • #7
You can simplify by taking [tex]Ame^{j\psi}[/tex] outside the integral sign.
The resultant integrand looks like the Fourier transform of the delta function.
 
  • #8
Are you sure you're copying it from the textbook correctly? Shouldn't amplitude ##Am## be with ##m## as a subscript (like in ##A_m## or something)? Can you just screenshot the page with equations (I doubt it is an actual screenshot from the textbook) or make a photo of it?
What is the name of the source and where in the source (page, equation number) one can find these equations?

Dale said:
After the third equal sign the expression loses its dependence on t, so that seems wrong.
Because it got buried in the notation like ##\phi(f)=2\pi f_0 t + \psi## (you can spot it somewhere at the end of this... mess). Not sure if it would help fully decipher it.
 
Last edited:

1. What is an inverse Fourier transform?

An inverse Fourier transform is a mathematical operation that converts a signal from the frequency domain to the time domain. It takes a complex function in the frequency domain and decomposes it into its constituent frequencies in the time domain.

2. Why is an inverse Fourier transform useful?

An inverse Fourier transform is useful because it allows us to analyze signals in the time domain, which is often more intuitive and easier to interpret than the frequency domain. It also enables us to manipulate and process signals using techniques such as filtering and convolution.

3. How is an inverse Fourier transform calculated?

An inverse Fourier transform is typically calculated using a mathematical formula or algorithm that takes into account the amplitude and phase of each frequency component of the signal. This involves integrating the signal over all frequencies to reconstruct the time-domain signal.

4. What is the difference between a forward and inverse Fourier transform?

A forward Fourier transform converts a signal from the time domain to the frequency domain, while an inverse Fourier transform converts a signal from the frequency domain back to the time domain. This process is reversible, meaning that the original signal can be reconstructed by performing a forward Fourier transform and then an inverse Fourier transform.

5. In what fields is the inverse Fourier transform commonly used?

The inverse Fourier transform is used in a wide range of fields, including signal processing, image processing, communications, and physics. It is also a fundamental tool in quantum mechanics, where it is used to describe the behavior of particles in terms of their wavefunctions.

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