Fourier transform
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- updated 17 Aug 2022:
Nothing to disclose
Updates to Article Attributes
Body
was changed:
Fourier transform is a mathematical operation which converts a time domain signal into a frequency domain signal5.
Discussion
Fourier transform is integral to all modern imaging, and is particularly important in MRI. The signal received at the detector (receiver coils in MRI, piezoelectric disc in ultrasound and detector array in CT) is a complex periodic signal made of a large number of constituent frequencies (i.e., bandwidth). This can be visualizedvisualised as multiple sine and or cosine waves along a time-axis. Fourier transform represents the same data over a frequency-axis. A common example is the MR spectroscopy image in which different molecules are at different frequencies along the x-axis.
History
French mathematician Joseph Fourier developed a method of decomposing a wave function into a series of sine waves in the 19th century 5.
-<p><strong>Fourier transform</strong> is a mathematical operation which converts a time domain signal into a frequency domain signal.</p><h4>Discussion</h4><p>Fourier transform is integral to all modern imaging, and is particularly important in MRI. The signal received at the detector (receiver coils in MRI, piezoelectric disc in ultrasound and detector array in CT) is a complex periodic signal made of a large number of constituent frequencies (i.e., bandwidth). This can be visualized as multiple sine and or cosine waves along a time-axis. Fourier transform represents the same data over a frequency-axis. A common example is the MR spectroscopy image in which different molecules are at different frequencies along the x-axis.</p>- +<p><strong>Fourier transform</strong> is a mathematical operation which converts a time domain signal into a frequency domain signal <sup>5</sup>.</p><h4>Discussion</h4><p>Fourier transform is integral to all modern imaging, and is particularly important in MRI. The signal received at the detector (receiver coils in MRI, piezoelectric disc in ultrasound and detector array in CT) is a complex periodic signal made of a large number of constituent frequencies (i.e., bandwidth). This can be visualised as multiple sine and or cosine waves along a time-axis. Fourier transform represents the same data over a frequency-axis. A common example is the MR spectroscopy image in which different molecules are at different frequencies along the x-axis.</p><h4>History</h4><p>French mathematician <strong>Joseph Fourier </strong>developed a method of decomposing a wave function into a series of sine waves in the 19th century <sup>5</sup>.</p>
References changed:
- 1. Allisy-Roberts P, Williams J. Farr's Physics for Medical Imaging. W.B. Saunders Company. (2007) ISBN:0702028444. Pages 81-82 <a href="http://books.google.com/books?vid=ISBN0702028444">Read it at Google Books</a> - <a href="http://www.amazon.com/gp/product/0702028444?ie=UTF8&tag=radiopaediaor-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0702028444">Find it at Amazon</a><div class="ref_v2"></div>
- 3. Mansfield P, Morris PG. NMR Imaging in Biomedicine. Elsevier. (1982) ISBN:0323154069. <a href="http://books.google.com/books?vid=ISBN0323154069">Read it at Google Books</a> - <a href="http://www.amazon.com/gp/product/0323154069">Find it at Amazon</a><span class="ref_v3"></span>
- 4. Bracewell RN. The Fourier transform. Sci. Am. 1989;260 (6): 86-9, 92-5. <a href="http://www.ncbi.nlm.nih.gov/pubmed/2727659">Pubmed citation</a><span class="ref_v3"></span>
- 5. Mahesh M. The Essential Physics of Medical Imaging, Third Edition. Med Phys. 2013;40(7):077301. Page 69.<a href="https://doi.org/10.1118/1.4811156">doi:10.1118/1.4811156</a> - <a href="https://www.ncbi.nlm.nih.gov/pubmed/28524933">Pubmed</a>
- 1. Allisy-Roberts P, Williams J. Farr's Physics for Medical Imaging. W.B. Saunders Company. (2007) ISBN:0702028444. <a href="http://books.google.com/books?vid=ISBN0702028444">Read it at Google Books</a> - <a href="http://www.amazon.com/gp/product/0702028444?ie=UTF8&tag=radiopaediaor-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0702028444">Find it at Amazon</a><div class="ref_v2"></div>
- Mansfield P, Morris PG. NMR Imaging in Biomedicine. Elsevier. (1982) ISBN:0323154069. <a href="http://books.google.com/books?vid=ISBN0323154069">Read it at Google Books</a> - <a href="http://www.amazon.com/gp/product/0323154069">Find it at Amazon</a><span class="ref_v3"></span>
- Bracewell RN. The Fourier transform. Sci. Am. 1989;260 (6): 86-9, 92-5. <a href="http://www.ncbi.nlm.nih.gov/pubmed/2727659">Pubmed citation</a><span class="ref_v3"></span>
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