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

1. Jul 28, 2011

### zheng89120

it seems like a pretty commonly used computational/mathematical method in analyzing experimental data, such as voltage signals

2. Jul 28, 2011

### gsal

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.

3. Jul 29, 2011

### xts

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.

4. Jul 29, 2011

### Delta Kilo

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

5. Jul 29, 2011

### mikeph

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.