Fourier and inverse fourier transform

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SUMMARY

The discussion focuses on the Fourier and inverse Fourier transforms, specifically the calculation methods and when to use definitions versus shortcuts. The user seeks resources for both theoretical understanding and problem-solving examples. They express a preference for deriving results from definitions but acknowledge the practicality of using tabular values for efficiency. The conversation emphasizes the importance of understanding foundational concepts while also recognizing the utility of established shortcuts.

PREREQUISITES
  • Understanding of Fourier Transform and Inverse Fourier Transform concepts
  • Familiarity with complex exponential functions, specifically e^-iwt
  • Knowledge of integration techniques relevant to transform calculations
  • Basic grasp of mathematical theorems related to Fourier analysis
NEXT STEPS
  • Explore resources on Fourier Transform properties and applications
  • Study examples of Fourier Transform calculations using both definitions and shortcuts
  • Learn about the convergence and limits of Fourier Transforms
  • Investigate advanced topics such as the Fast Fourier Transform (FFT) algorithm
USEFUL FOR

Students and professionals in mathematics, engineering, and physics who are looking to deepen their understanding of Fourier analysis and its applications in various fields.

goohu
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Hi, I've been looking all over the net for good examples but I've only found some intro but no examples being solved.

If you know of good resources (both theories and problems) please let me know!

View attachment 9435

a) Calculate Fourier and inverse Fourier transform of f(t).
b) Calculate the limit.

My question is :
it looks like sometimes you use the definition of the transform with the integration of f(t) * e^-iwt ,
other times you use shortcuts from formula sheets. Any tips of when to use which?

I'm pretty clueless about this one right now , is it okay to just ask for a solution with explanation?
 

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I use the way, which I like more. Sometimes I'm "lazy" and take tabular values, sometimes I derive the results from definitions and theorems. So, do what suits you, your needs and situation! It's good to know, how the most essential results are derived, but it's not necessarily required to derive everything again in the case of new problem.
 
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