A Tough Fourier Transform (for me)

In summary: I found that link. I think I understand the concept now and will try it. In summary, the problem is that I don't know how to solve a standard Gaussian equation.
  • #1
jaurandt
24
0
Attached is a personal problem that I spent last night working on for about 2 hours and something is going wrong, I just can not figure it out what. The answer by the big X is what I wound up with but it's obviously not correct. Could someone please guide me through solving this? The starting problem is on the top left, the correct answer is boxed on the top right.
IMG_20190508_120613086~2.jpg
 
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  • #3
PeterDonis said:
Please use the PF LaTeX feature to post your equations directly in the thread. Per PF rules, equations should not be posted as images, as that makes it impossible to quote them in replies.

Help on the LaTeX feature can be found here:

https://www.physicsforums.com/help/latexhelp/

Sorry, I will do so from now on. But what's most important to me is the problem for the sake of my sanity...
 
  • #5

1. What is a Fourier Transform?

A Fourier Transform is a mathematical tool used to analyze the frequency components of a signal. It decomposes a signal into its individual frequency components, allowing for a better understanding of the underlying patterns and trends within the signal.

2. Why is the Fourier Transform important?

The Fourier Transform is important because it is widely used in many scientific and engineering fields, including signal processing, image and audio analysis, and quantum mechanics. It allows for a deeper understanding of complex signals and systems, and is essential in solving many real-world problems.

3. How does the Fourier Transform work?

The Fourier Transform works by breaking down a signal into a series of sinusoidal functions of different frequencies and amplitudes. These sinusoidal functions are then combined to reconstruct the original signal. The Fourier Transform can be performed using mathematical equations or through digital algorithms.

4. What is the difference between the Fourier Transform and the Inverse Fourier Transform?

The Fourier Transform converts a signal from the time domain to the frequency domain, while the Inverse Fourier Transform converts it back from the frequency domain to the time domain. Essentially, the Fourier Transform breaks down a signal into its frequency components, while the Inverse Fourier Transform combines these components to reconstruct the original signal.

5. Are there any limitations to the Fourier Transform?

While the Fourier Transform is a powerful tool, it does have limitations. It assumes that the signal is periodic and infinite, which may not always be the case in real-world scenarios. Additionally, the Fourier Transform can only analyze signals with a finite number of frequency components, so it may not be suitable for highly complex signals with an infinite number of frequencies.

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