2017 Imaging for Physicists Coursebook

Fourier Transform (FT)

• Time signal can be decomposed into sum of sinusoids of different frequencies, phases and amplitudes

s(t) = a

+ a

sin(  1

t +  1

) + a

sin(  2

t +  2

) + …

0

1

2

• Fourier series may be represented by frequency spectrum • Time and frequency domain data can be thought of as FT pairs