Fourier expansion

  1. Use the Fourier expansion for a square wave to generate three plots estimating a square waveform of unit amplitude. The only difference between the three plots is the number of terms retained in the Fourier expansion, either 3 terms, 6 terms, or 9 terms.

Here is a good place to start: https://en.wikipedia.org/wiki/Square_wave

This work can be done in MatLab or in Excel. The MatLab code or excel spreadsheet will need to be handed in for credit, along with printouts of the three plots.

(This problem is intended to demonstrate that complex waveforms, even with sharp changes in the y-amplitudes over small changes along the x-axis, can be approximated fairly well using a finite series of sinusoids. This same concept enables the interferogram obtained by FTIR to be converted into a set of sinusoids, each representing light of a particular frequency. The amplitude of each sinusoid is related to the intensity of a particular frequency in the spectrum, which is obtained after Fourier transformation.)

  1. a) Calculate how far the moving mirror would have to move in a Michelson interferometer in order to meet the Nyquist sampling limit for the spectral range between 500 cm-1 and3000 cm-1. The Nyquist condition requires at least 2 data points to be measured for one period of an oscillation.
  2. b) How many data points should be collected over this distance?

 

Last Updated on February 11, 2019 by Essay Pro