{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
BCMB/CHEM 8190 Data Acquisition and Processing Fourier Transformation
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
Visualization of FT My time (t) Frequency ( ω ) S(k-1) S(k) S(k+1) = + + (k+1) k (k-1) FT
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 4
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
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 ° phase shift of pulse and receiver eliminates Another artifact is a quadrature image. Cycling x and y channels Along with a 90 ° phase shift of the pulses eliminates this (cyclops) =
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern