Fourier Transform question F o sin(10t)

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SUMMARY

The Fourier Transform of the sine function sin(10t) results in two delta functions located at ±\(\frac{10}{2\pi}\). The discussion emphasizes the importance of understanding the manual derivation of the Fourier Transform rather than relying solely on tables. Additionally, the concept of frequency shifting using the formula \(e^{j 2\pi f_c t}g(t) \leftrightarrow G(f - f_c)\) is highlighted as a crucial step in manipulating the transform for further analysis.

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  • Understanding of Fourier Transform principles
  • Familiarity with delta functions in signal processing
  • Knowledge of frequency shifting techniques
  • Basic proficiency in complex exponential functions
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  • Study the derivation of the Fourier Transform for sine functions
  • Explore delta functions and their properties in signal processing
  • Learn about frequency shifting and its applications in signal analysis
  • Investigate the use of Fourier Transform tables and their limitations
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Students and professionals in electrical engineering, signal processing, and applied mathematics who are looking to deepen their understanding of Fourier Transforms and their applications in analyzing periodic signals.

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Fourier Transform of sin(10t)

Hi all,
Can some1 explain how to get the complex Fourier transform of sin(10t)

I understand how to steal it off a Fourier transform table, but i have no idea how to do it manually.

Any help anyone?
Cheers
 

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The Fourier transform of a pure tone (the sine function) is two delta function, one at +\frac{10}{2\pi} and the other at -\frac{10}{2\pi} (I could have my {2\pi}'s wrong). The last part of this question should be a simple sampling in the frequency domain of the transform of the function in part A.
 
thanks for your reply.
yeah i was way off. Thanks for the clarification
 
Hi,
When answering question above, you stated the need "The last part of this question should be a simple sampling in the frequency domain of the transform of the function in part A."

I believe i have the right rule attached.

e^(j 2pi fc t)g(t) <-> G(f-fc) (this formula is attached in jpeg)

So, once i find the Fourier transform of the first function. I simply need to shift it by fc.

I have had a go at it, i think its right. (answer attached)

If you could point me in the right direction, that'd be great. cheers
 

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