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