How do we get a spectrum?

  A spectrum is just another way of looking at vibration. Let's say we mount
a vibration sensor (S) on a vibrating machine (they all vibrate). If we were to
take the output of that sensor and pass it through a filter to reject the very
high frequencies and the very low frequencies, we could look at the signal on an
oscilloscope.

  The oscilloscope picture shows us the amplitude of the vibration as it varies in
time. This view, known as the time domain, would show us that the normal
vibration signal from the typical machine is fairly complex. In order to begin to
extract information from this signal, we might measure the peak vibration.
We can also measure the root mean square of the signal, known as rms.
These two measures are the two most fundamental, and can be obtained with a
simple hand-held meter.

  In order to obtain the vibration spectrum of the data, we must transform the
signal into the frequency domain. To do this, we first digitize the signal
(as in music on a compact disk) by rapidly sampling the vibration amplitude at a
fixed time rate. We will store these values in a array or list in a computer.
(so now we need a computer).

  Now that we have this list in the memory of our computer, we can perform a
process that will transform the list into the frequency domain. This process
is the Fast Fourier Transform, or FFT. The FFT is a destructive transform,
that is it replaces the time amplitudes in the list with frequency amplitudes.
Now we have a list of vibration amplitude as it varies with frequency.

Now, lets plot the list of vibration amplitudes vs. frequency.

  Since we're just looking at the same vibration two different ways, we should
be able to draw some equivilencies between the time domain and the frequency
domain.

  In the frequency domain, the amplitude spectral peak closely approximates the
value of the peak in the time domain. The total area under the spectral curve is
equal to the rms value of the time domain data.

So a spectrum is just a different view of time-varying vibration.