# Fourier analysis

(a) Explain the relationship between the spectral components indicated above and the corresponding graph showing the motion of the surface of the motor plotted as a function of time. What do they represent?

(b) Given the amplitudes indicated in the above diagram, copy and complete the table below for the amplitude of the vibration in the time domain. Sketch the result of your reconstructed waveform in the period 0 < t < 0.1 ms, assuming

f0 = 5000 Hz.

See attached file for full problem description.

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#### Solution Preview

Please see attached file.

First you need to understand the Fourier Theorem. It says that a wave in the time domain, no matter how complex it looks can be transformed into an infinite sum of sinusoidals of single frequency and unique amplitude as depicted in the following figure:

The graph in the time domain is only one which tells you how the motor in vibrating as a whole where you have vibration amplitude versus time. That is you have a function of time f(t). Now in the Fourier transformed space what you see in graphs are the amplitude spectrum of the sinusoidal components which are present in your signal and the phase spectrum ...

#### Solution Summary

This shows how to explain the relationship between given spectral components and to complete a table for the amplitude of vibration in time.