What is the purpose/significance of doing a FFT on a signal?

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Discussion Overview

The discussion revolves around the purpose and significance of performing a Fast Fourier Transform (FFT) on signals, particularly in the context of analyzing experimental data, such as voltage signals. Participants explore various applications and implications of FFT in different fields, including electronics, mechanical systems, and data compression.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that FFT is a commonly used method for analyzing experimental data, particularly voltage signals.
  • It is suggested that FFT helps in decomposing a signal into sinusoidal components of various amplitudes and frequencies.
  • One participant explains that FFT is an efficient algorithm for computing the discrete Fourier transformation, allowing for the representation of complex signals as sums of sinusoidal functions.
  • There is a mention of linear systems responding to sinusoidal stimulation, which simplifies theoretical analysis.
  • Another participant highlights that FFT reveals the frequency spectrum of a signal, making it easier to identify weak periodic signals amidst noise.
  • It is proposed that operations in the frequency domain, such as correlation, can be more straightforward compared to the time domain.
  • One participant points out the utility of FFT in data compression, particularly for signals that are nearly sinusoidal, suggesting its application in image and sound compression algorithms.

Areas of Agreement / Disagreement

Participants generally agree on the utility of FFT in signal analysis and various applications; however, the discussion includes multiple perspectives on its significance and specific uses, indicating that there is no single consensus on its purpose.

Contextual Notes

The discussion does not resolve the limitations or assumptions underlying the applications of FFT, such as the conditions under which it is most effective or the specific types of signals that benefit most from this analysis.

zheng89120
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it seems like a pretty commonly used computational/mathematical method in analyzing experimental data, such as voltage signals
 
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it is used to figure out what a signal consists of...you know, by decomposing it into a bunch of sinusoidal of various amplitudes and frequencies.
 
FFT is just a computer algorithm to efficiently compute discrete Fourier transformation - represent given signal of weird shape as a sum of sinusoidal ones.
Most of electronic systems are:
1. linear - they response to sum of signals is equal to sum of responses to individual ones;
2. they response to sinusoidal stimulation is also a sinusoid of the same frequency (just amplitude is changed and phase shifted) - easy to analyse theoretically

So if you want to analyse its behaviour, you may first decompose your input signal as a sum of sinusoidal signals, compute the system response to every one of them, then sum the resulting sinusoidal signals again.

The same approach may apply not only to electronics, but also to many other fields - e.g. vibrations of mechanical systems, acoustics, etc.
 
zheng89120 said:
it seems like a pretty commonly used computational/mathematical method in analyzing experimental data, such as voltage signals
1. It shows you the frequency spectrum. Like the one on Cisco logo :)
2. If you are looking for weak periodic signals among the noise, they will show up as spikes on frequency plot. Also it's easy to suppress unwanted periodic signals interfering with data.
3. Many common operations are much easier in frequency domain, correlation being prime example.
etc. etc.

DK
 
It's also very useful in data compression, particularly if your analogue signal is very nearly a sinusoid anyway. A whole time series (lots of data) can be compressed to a very small number of amplitudes in the frequency domain. I'm pretty sure the FFT is used in most image/sound compression algorithms.
 

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