- #1
Fourier Transform question F o sin(10t)
- Context: Undergrad
- Thread starter priscared
- Start date
Click For Summary
Discussion Overview
The discussion centers on the calculation of the complex Fourier transform of the function sin(10t). Participants explore both the theoretical aspects of the Fourier transform and practical steps for manual computation, including the application of specific rules related to frequency shifting.
Discussion Character
- Exploratory, Technical explanation, Mathematical reasoning
Main Points Raised
- One participant requests clarification on how to manually compute the Fourier transform of sin(10t), indicating a reliance on transform tables.
- Another participant asserts that the Fourier transform of sin(10t) results in two delta functions located at +10/(2π) and -10/(2π), though they express uncertainty about the correctness of the 2π factors.
- A subsequent reply acknowledges the previous participant's clarification and admits to being incorrect in their understanding.
- A different participant introduces a frequency shifting rule related to the Fourier transform, suggesting that after finding the transform of sin(10t), they can apply this rule to shift the result by a specified frequency fc.
- This participant expresses a desire for feedback on their approach and shares their work for review.
Areas of Agreement / Disagreement
There is no consensus on the correct application of the Fourier transform for sin(10t), as participants express varying levels of understanding and correctness in their claims. Multiple viewpoints and methods are presented without resolution.
Contextual Notes
Participants reference specific formulas and transformations but do not fully resolve the mathematical steps or assumptions involved in their calculations.
- #2
daviddoria
- 96
- 0
The Fourier transform of a pure tone (the sine function) is two delta function, one at [tex]+\frac{10}{2\pi}[/tex] and the other at [tex]-\frac{10}{2\pi}[/tex] (I could have my [tex]{2\pi}[/tex]'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.
- #3
priscared
- 11
- 0
thanks for your reply.
yeah i was way off. Thanks for the clarification
yeah i was way off. Thanks for the clarification
- #4
priscared
- 11
- 0
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
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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