# Fourier Transformation of Data

## 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.

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

1. What is the νmax that corresponds to the sampling rate for this instrument?

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

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

1. 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.

1. Is there any danger to the change you proposed above?

## Exercise 2 – Frequency Ranges and Noise

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

1. 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 νmax?

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