Fourier Transform Applied to NMR

Click For Summary
SUMMARY

The discussion centers on the application of the Fourier Transform in converting time domain graphs to frequency domain graphs, specifically in the context of NMR (Nuclear Magnetic Resonance) and MRI (Magnetic Resonance Imaging). The user seeks examples and graphical representations of the Fourier Transform, highlighting the distinction between real and imaginary components. The conversation emphasizes the importance of understanding both the Fourier Transform and its sine and cosine variants for a comprehensive grasp of periodic functions.

PREREQUISITES
  • Understanding of Fourier Transform principles
  • Familiarity with periodic functions
  • Basic knowledge of NMR and MRI concepts
  • Graphical representation of mathematical functions
NEXT STEPS
  • Explore online resources for "Fourier Transform Tutorial" to grasp foundational concepts
  • Study the differences between Fourier Transform, Fourier Sine Transform, and Fourier Cosine Transform
  • Utilize online calculators to visualize Fourier Transforms of various functions
  • Research graphical interpretation of real and imaginary parts of Fourier Transforms
USEFUL FOR

Chemistry students, physicists, and anyone involved in NMR and MRI applications who seeks to deepen their understanding of Fourier Transforms and their graphical representations.

dsnel23
Messages
2
Reaction score
0

Homework Statement



Hi, I'm taking a Chemistry NMR & MRI class and were going over the part where the time domain graph is converted to the frequency domain graph by way of the Fourier Transform. I took Applied Mathematics last semester and we spent a week on the Fourier Transform but no time on the Fourier sine or cosine transform.

From what I can tell, all periodic functions can be described as a sum of sine and cosine functions. The Fourier Transform of this can be divided into a real and imaginary part.

Does anyone have an example or two of say an expression before and after? And if possible a graph before and after? Like which part is the real and which the imaginary? If I'm wrong somewhere here I apologize and let me know please.

Thanks for any input!


Homework Equations





The Attempt at a Solution


 
Physics news on Phys.org
You might type "Fourier Transform Tutorial" into google. There are lots of sites that cover FT basics, and even online calculators where you can enter functions and see their transforms right away. Come back here if you still have questions.
 

Similar threads

Fourier Transform - Solutions Error?
  • · Replies 5 ·
Replies
5
Views
2K
Fourier sine and cosine transforms of Heaviside function
  • · Replies 2 ·
Replies
2
Views
3K
Fourier transform: duality property and convolution
  • · Replies 1 ·
Replies
1
Views
2K
Fourier transform: signal with filter
  • · Replies 3 ·
Replies
3
Views
2K
Fourier transform of a shifted and time-reversed sign
  • · Replies 5 ·
Replies
5
Views
3K
Fourier Transformation of ODE
  • · Replies 2 ·
Replies
2
Views
2K
Fourier transform of exponential function
  • · Replies 3 ·
Replies
3
Views
3K
Steady wave eq and fourier transform
  • · Replies 1 ·
Replies
1
Views
1K
Fourier Transform and Parseval's Theorem
  • · Replies 7 ·
Replies
7
Views
2K
Applying Convolution to a PDE with a Fourier Transform
  • · Replies 12 ·
Replies
12
Views
2K