Fourier transform

Last revised by Candace Makeda Moore on 18 Feb 2024

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 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 are the MR spectroscopy 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.

ADVERTISEMENT: Supporters see fewer/no ads

Updating… Please wait.

 Unable to process the form. Check for errors and try again.

 Thank you for updating your details.