Understanding the Significance of Fourier Analysis in Signal Processing

[Jon.G]

Ok so this isn't a homework question per se, but I'm currently writing a report on Fourier Analysis but a bit stuck as to what the results can actually help with. I realized that I don't grasp how a Fourier Transform can be used.

In the experiment we recorded the signal created by a remote control when a button was pressed and, using LabView, plotted the Fourier transform.
The peak was at around 4000Hz, with the next noticeable one coming in at around 8000Hz (still much smaller than the peak at 4000, I'm thinking this might be a harmonic?)
What can I do with this information?
How does knowing that signal operates at a frequency of 4000Hz allow me to analyse/study/improve the system?

Thanks

 

[OldEngr63]

Sounds like you are performing an FFT or similar digital transformation on the data set. What this give you, strictly speaking, is the coefficients of a Fourier Series, not a Fourier Transform. You should be able to find a ton of information on Fourier Series with a little bit of searching on the net. I suggest that you start there.

 

[rude man]

What it does is take your finite-duration signal, assume it repeats infinitely in positive and negative time, then computes the Fourier series coefficients.

The lowest-frequency coefficient (the "fundamental") is at frequency = 1/T where T is the duration of your signal. So if your lowest frequency component was 4000 Hz then either you sampled a stretch of signal T = 1/4000 sec.
or there was no energy in the signal below 4000 Hz. The former is probable.

The significance is that you now have a spectrum of the sampled signal providing you're happy with the lowest detectable component being 1/T. Note that the Fourier series of a periodic signal is valid over all t including the interval 0 < t < T.