Re: Fourier transform and oscillation amplitude


Pygmalion wrote:
Howdy mathematicians!

How can one obtain the oscillation amplitude from the Fourier spectrum?
This question is trivial if discrete Fourier transform has value
different than zero only for one frequency. However, usually Fourier
transform looks something like that:

6.0 Hz - 1 mm
6.1 Hz - 10 mm
6.2 Hz - 40 mm
6.4 Hz - 5 mm

What is the amplitude of oscillation in that case?

If "mm" means "millimeters", that sounds like a strange unit
for a Fourier transform.

You are looking at a signal with some bandwidth. You
could estimate the total energy in that signal by adding
up the energy at each discrete frequency point in the
signal (energy is magnitude squared of the FT). This
would be the same as the total energy of your original
signal.

However, since you have a signal with bandwidth, the
relationship between amplitude and energy is not
so simple, without additional information. Is it a
constant amplitude signal for instance? Is this just
a pure sine wave that got spread because the time window
was not an integral number of periods?

Finally, there are some arbitrary scale factors that
different versions of the FT use.

Probably the best thing for you to do is calibrate your
FT. Run a signal of known amplitude through it and
measure the total energy across the measured band,
in your units.

Also, if 40 mm represents a peak, what is a correct name the whole
structure?

I've heard "peak". "There is a broad peak at 50 kHz, and a very
sharp peak at 35 kHz..." I don't know if there's any formal word
in common usage.

- Randy

.

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