FT_and_Processing_10

FT_and_Processing_10 - BCMB/CHEM 8190 Data Acquisition and...

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BCMB/CHEM 8190 Data Acquisition and Processing Fourier Transformation
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S( ω ) = S(t) exp(-i ω t) dt = S(t) (cos( ω t) – i sin( ω t))dt S(k/(dtN)) = S(jdt) exp(-i2 π j (k/dtN)), -N/2 < j < N/2 Fourier Transformation My time (t) Frequency ( ω ) FT - - J=0 N-1
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Visualization of FT My time (t) Frequency ( ω ) S(k-1) S(k) S(k+1) = + + (k+1) k (k-1) FT
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Lorenzian Lines S( ω ) = (M 0 T 2 ) / (1 + T 2 2 ( ω 0 - ω ) 2 ) Frequency ( ω ) ω 0 At ½ height, T 2 2 ( ω 0 - ω ) 2 = 1 Implies Δω 1/2 = 2/T 2 , Δν 1/2 = 1/( π T 2 ) Signal is maximum at ω 0
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Digitizing Data and Setting Sweep Widths (sw) Data points define frequency well Nyquist frequency – minimum points Ambiguities arise at higher frequencies Note: pattern of points is the same sw real spectrum observed spectrum
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Phase Cycling Reduces Artifacts One artifact is a glitch at zero frequency (middle of spectrum). This can come from a DC imbalance of quadrature channels. Adding scans with 180
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This note was uploaded on 11/07/2011 for the course CHEM 8853R taught by Professor Gelbaum during the Fall '11 term at Georgia Tech.

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FT_and_Processing_10 - BCMB/CHEM 8190 Data Acquisition and...

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