Fourier transform
Updates to Article Attributes
Fourier transform is a mathematical operation which converts a time domain signal into a frequency domain signal 5.
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 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 isare the MR spectroscopy image images 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 <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>- +<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 are the <a href="/articles/mr-spectroscopy-1" title="MR spectroscopy">MR spectroscopy</a> images 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>