lec34_12112006 - 10.34, Numerical Methods Applied to...

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10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #34: Fourier Transforms and Fast Fourier Transforms (FFT). Fourier Analysis / Transforms Basis Set Methods () imx m m m m m m m m m e mx x mx x c x f = = = = = φ φλφ ) cos( ) sin( ) ( 2 2 Convolution Integral ττ τ d t h g h g ) ( ) ( * ) ( ˆ ) ( ˆ ) * ( ˆ h F g F h g F = Correlation (g,h) + d h t g ) ( ) ( [ * ) ( ˆ ) ( ˆ ) , ( n Correlatio ˆ h F g F h g F = ] Å complex conjugate Quantum Mechanics Ψ (x) = e ikx Å state of definite momentum p x = ħ k Ψ ( φ ) = e im Φ Å definite angular momentum J Φ = ħ m Spectroscopy ν = Δ E / h pulsed NMR: time domain measurement of I( ν ) FTIR: I l Figure 1. Diagram showing the path of light in an FTIR. Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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These methods are powerful, but require a computer to interpret the results
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.

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lec34_12112006 - 10.34, Numerical Methods Applied to...

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