# Fourier Transformation of Data

- Page ID
- 291565

## Exercise 1 – Sampling Rate (SR), Acquisition Time (AQ), and Number of Data Points (NDP)

A type of instrument called a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer (FT-ICR-MS) costs about the same as a nice NMR ($500k) and is used in a variety of applications where ultra-high resolution mass information is required. The FT-ICR-MS at the Woods Hole Oceanographic Institution (pictured below) uses a sampling rate of 500 kHz and FT to produce a mass spectrum from a digitized complex waveform containing 65,536 data points in the time domain. The complex waveform contains information about ion cycling frequencies, which are in turn connected directly to ion *m/z* ratios.

- When we say the FT-ICR-MS has a sampling rate of 500 kHz, describe what is being sampled?

- What is the ν
_{max}that corresponds to the sampling rate for this instrument?

- Calculate the acquisition time for a raw FT-ICR-MS data file.

- Calculate the digital resolution (Δν) for the FT-ICR-MS.

- How would you change the settings to increase the digital resolution of the FT-ICR-MS? You may reasonably assume that the size of data files is determined by the hardware/software and thus can’t be changed.

- Is there any danger to the change you proposed above?

## Exercise 2 – Frequency Ranges and Noise

- Does sampling rate influence the range of frequencies that you can detect using FT-NMR? Explain briefly.

- What would be the problem if a background signal due to noise (that was necessarily a component of the raw FID) had a characteristic frequency that exceeded ν
_{max}?

- How would you solve this problem if you were the person responsible for instrument design?

## Contributors and Attributions

- David Griffith, Willamette University (dgriffit@willamette.edu)
- Sourced from the Analytical Sciences Digital Library