Fourier and inverse fourier transform

In summary, The speaker is looking for good resources for examples and theories on calculating Fourier and inverse Fourier transforms and limits. They also ask for tips on when to use different methods and express that they sometimes use shortcuts or tabular values rather than deriving results from definitions and theorems. They end by stating that it's important to understand how to derive essential results, but it's not always necessary to do so for every problem.
  • #1
goohu
54
3
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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  • #2
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.
 
  • #3
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FAQ: Fourier and inverse fourier transform

What is Fourier transform and why is it important in science?

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies. It is important in science because it allows us to analyze and understand complex signals and systems in terms of their frequency components.

What is the difference between Fourier transform and inverse Fourier transform?

The Fourier transform converts a time domain signal into its frequency domain representation, while the inverse Fourier transform does the opposite - it converts a frequency domain signal back into its time domain representation.

What is the relationship between Fourier transform and Fourier series?

Fourier series is a special case of Fourier transform, where the signal being analyzed is periodic. Fourier transform can be thought of as an extension of Fourier series to non-periodic signals.

How is Fourier transform used in signal processing and image analysis?

Fourier transform is widely used in signal processing and image analysis to filter out noise, enhance certain frequencies, and extract useful information from signals and images.

Are there any limitations to using Fourier transform?

Yes, there are some limitations to using Fourier transform. It assumes that the signal being analyzed is stationary, meaning it does not change over time. It also assumes that the signal is infinitely long, which may not be true for real-world signals. Additionally, Fourier transform may not be suitable for signals with sharp discontinuities or spikes.

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