How MRI Works - Part 3 - Fourier Transform and K-Space

How MRI works, Part 3 - The Fourier Transform and k-Space

Part 1 - NMR Basics: https://youtu.be/TQegSF4ZiIQ
Part 2 - Spin Echo: https://youtu.be/M7yh0To6Wbs
Part 4 - The Gradient Echo Sequence :https://youtu.be/vapJRr6gAds

FFT code: https://github.com/thePIRL/fft-code-for-fun/blob/main/FFT%20code

Powerpoint slides from this lecture can be purchased here:
https://www.patreon.com/thePIRL769/shop/powerpoint-slides-how-mri-works-part-3-62224?source=storefront

0:00 - Intro
1:00 - The Sinusoid and phasors
5:48 - Fourier Theory
9:05 - The Fourier Transform and Inverse Fourier Transform
11:10 - Adding phase to our plots
13:42 - Fourier transform of sin(w0t)
17:40 - Hermitian Fourier transforms
19:26 - The Dirac Delta Function

21:00 - Fourier Transform Examples:
21:48 - Decaying Exponential/Lorentzian
29:09 - Square Pulse/Sinc Function
31:08 - Gaussian/Gaussian and Fourier Shift
32:39 - Discrete Signals, Fourier Transforms, and Nyquist
36:12 - The Fast Fourier Transform

40:26 - kSpace
40:48 - t/w and x/k convention
41:55 - Intro to kSpace
48:05 - Hermitian kSpace, half Fourier, and spatial filtering
51:29 - kSpace frequency units
55:08 - FFT organization of kSpace

56:56 - Outro and GRE Teaser

Drinking game: Take a drink every time I say 'notice'

Do I talk too fast in this one?
#some2