# How to detect oscillations/characteristic frequencies in data?
**URL:** https://discourse.julialang.org/t/how-to-detect-oscillations-characteristic-frequencies-in-data/105169
**Category:** Signal and Image Processing
**Tags:** dsp, fft
**Created:** [October 19, 2023, 9:47am UTC](https://discourse.julialang.org/t/how-to-detect-oscillations-characteristic-frequencies-in-data/105169 "2023-10-19T09:47:32Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@Torkel](https://discourse.julialang.org/u/Torkel)
#### Post date: [October 19, 2023, 9:47am UTC](https://discourse.julialang.org/t/how-to-detect-oscillations-characteristic-frequencies-in-data/105169/1 "2023-10-19T09:47:32Z")
I have a (many) signal I have gotten from experiments. The extent can be argued, but I’d definitely say there is _something_ pulsing/oscillatory going on:
```julia
using Plots
plot(signal)
```
How do I actually show this though? I have tried to use the welch periodogram. However, it mainly seems to show a peak at 0 (which is what you’d expect from white noise, right?):
```julia
using DSP
wpd = welch_pgram(signal, 300)
plot(wpd.freq, wpd.power)
```
Removing the mean have little effect:
```julia
signal2 = signal ./ mean(signal)
wpd2 = welch_pgram(signal2, 300)
plot(wpd2.freq, wpd2.power)
```
Ideally, I was hoping one peak only, at a non-zero frequency, corresponding to the frequency of the pulsing. Am I right that the periodogram seems to suggest my signal is mostly noise?
Is there a go-to function/approach in Julia to determine whether there is an oscillatory behaviour going on? I was thinking maybe something like [Signal-to-noise ratio - MATLAB snr](https://www.mathworks.com/help/signal/ref/snr.html)
---
### Author:  [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [October 19, 2023, 9:56am UTC](https://discourse.julialang.org/t/how-to-detect-oscillations-characteristic-frequencies-in-data/105169/2 "2023-10-19T09:56:32Z")
This looks to me like a chaotic spiky oscillator. I wouldn’t put to much attention on signal 2 noise ration, because it seems that there is almost no noise. ~~I am not sure what `welch` does, but it seems incorrect… What does the standard FFT power spectrum show (after removing mean)?~~ EDIT: I didn’t see that the mean was divided, I assumed it was subtracted without looking at the code. Welsch works fine.
If neither work, you can try some of the methods in this function to get the dominant period: [Fixed points & Periodicity · ChaosTools.jl](https://juliadynamics.github.io/ChaosTools.jl/stable/periodicity/#Estimating-the-Period)
---
### Author:  [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)
#### Post date: [October 19, 2023, 10:03am UTC](https://discourse.julialang.org/t/how-to-detect-oscillations-characteristic-frequencies-in-data/105169/3 "2023-10-19T10:03:47Z")
> [@Torkel](#):
>
> Removing the mean have little effect:
You should subtract, not divide!
PS:
Check out the [EasyFFTs package](https://discourse.julialang.org/t/ann-announcing-easyffts-jl/90174).
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [October 19, 2023, 12:47pm UTC](https://discourse.julialang.org/t/how-to-detect-oscillations-characteristic-frequencies-in-data/105169/4 "2023-10-19T12:47:40Z")
As said above, you want to _subtract_ the mean. You typically also want to plot the spectrum with a logarithmic y-axis, often also logarithmic x-axis.
---
### Author:  [@mike.ingold](https://discourse.julialang.org/u/mike.ingold)
#### Post date: [October 19, 2023, 2:03pm UTC](https://discourse.julialang.org/t/how-to-detect-oscillations-characteristic-frequencies-in-data/105169/5 "2023-10-19T14:03:19Z")
> [@Torkel](#):
>
> I have tried to use the welch periodogram. However, it mainly seems to show a peak at 0 (which is what you’d expect from white noise, right?)
Power at 0 Hz is caused by a non-zero mean. Since your data is all non-negative, this is basically guaranteed. Dividing the source signal by its mean really just normalizes the mean of the new signal; subtracting the mean will zero it.
```julia
signal2 = signal ./ mean(signal)
# mean(signal2) ≈ 1.0
signal2 = signal .- mean(signal)
# mean(signal2) ≈ 0.0
```
---
### Author:  [@Torkel](https://discourse.julialang.org/u/Torkel)
#### Post date: [October 19, 2023, 7:37pm UTC](https://discourse.julialang.org/t/how-to-detect-oscillations-characteristic-frequencies-in-data/105169/6 "2023-10-19T19:37:33Z")
Thanks everyone!
Substracting the mean did indeed give a more meaningful result:
ChaosTools sounds like it might be worth trying, I will give it a look.