Fluid Interface Frequency Transform

[member 428835]

Hi PF!

Fluid lies in a 2D rectangular channel and oscillates from a disturbance. I have several .csv files, each corresponding to a moment in time, where within each are two lists of numbers: the $x$ and $y$ position of a fluid interface. I'd like to decompose the interface into it's fundamental frequencies and amplitudes, like a Fourier transform. Any recommendation on where to look or broad idea what to do? Should I look for a single point on the interface or use the entire interface?

Picture attached for help seeing this.

 

[boneh3ad]

Whether you use the whole interface or a single point as it evolves in time depends on whether you're looking for temporal frequency or spatial wavenumber. You could, in principle, do a 2D spatiotemporal transform as well. It all depends on your goals.

 

[hutchphd]

How big are the files (how many points x) and how many time slices do you have? Excel will do this.

 

[member 428835]

Thank you both! I'm actually going to use the fft function in MATLAB for each point in time. I think this should work.

 

[boneh3ad]

It should but it's a question of what end result you are seeking and whether your data supports doing something like that. You may be limited by the number of points in your effective time series.

 

[member 428835]

It should but it's a question of what end result you are seeking and whether your data supports doing something like that. You may be limited by the number of points in your effective time series.

The first image I attached is an oscillation, and I have several several frames corresponding to different times. Knowing this, what kinds of questions do you raise as to whether or not the fft would work?

 

[hutchphd]

The issue is likely to be the sampling rate and amount of data for the time sequence. Also the FFT will assume fixed sampling interval.
The resolution in temporal and spatial frequencies is limited strictly by Nyquist.

 

[boneh3ad]

The first image I attached is an oscillation, and I have several several frames corresponding to different times. Knowing this, what kinds of questions do you raise as to whether or not the fft would work?

"Several frames" is not generally enough to form an effective time series. The frequency resolution of your Fourier transform is directly related to the number of points in time in your time series. The effective sampling rate will set the maximum frequency you can resolves, and the total length (in time) of your series will set the minimum frequency you can resolves. These will all be severely limiting issues if you don't have many points.

 

[member 428835]

Thanks!

 

[member 428835]

The issue is likely to be the sampling rate and amount of data for the time sequence. Also the FFT will assume fixed sampling interval.
The resolution in temporal and spatial frequencies is limited strictly by Nyquist.

So I'm kind of confused on the Nyquist frequency. I'm sampling a signal and it looks like this:

The sampling rate is 1 Hz, so every second. How would I calculate the Nyquist frequency?

 

[boneh3ad]

http://mathworld.wolfram.com/NyquistFrequency.html

 

[member 428835]

http://mathworld.wolfram.com/NyquistFrequency.html

I saw this, but what's the highest waveform?

 

[boneh3ad]

I saw this, but what's the highest waveform?

Ignore that part. Start with "The Nyquist frequency..."

It's just half the sampling rate and represents the highest resolvable frequency in a signal due to sampling. Frequencies above Nyquist will be aliases.

 

[member 428835]

Ignore that part. Start with "The Nyquist frequency..."

It's just half the sampling rate and represents the highest resolvable frequency in a signal due to sampling. Frequencies above Nyquist will be aliases.

Okay, so I'm sampling at 1 fps, so any recorded frequency above 1/2 fps is unreliable?

 

[boneh3ad]

It's not unreliable. It's unresolvable. There is a reason that your spectrum only exists out to 0.5 Hz. What isn't as obvious is that any frequency that is higher than Nyquist is still showing up in that spectrum as an alias, meaning you could have meaningful error due to aliasing if you don't take steps to do anti-aliasing filtering.

 

[member 428835]

It's not unreliable. It's unresolvable. There is a reason that your spectrum only exists out to 0.5 Hz. What isn't as obvious is that any frequency that is higher than Nyquist is still showing up in that spectrum as an alias, meaning you could have meaningful error due to aliasing if you don't take steps to do anti-aliasing filtering.

Can you elaborate on the final sentence? There isn't a frequency showing higher than Nyquist in my plot, right?

 

[boneh3ad]

Do a bit of background reading on aliasing. Your plot does not go past the Nyquist frequency, but aliases of higher frequencies can and do show up at lower frequencies if not addressed.