butterworth filter - given only cut-off frequency, how to decide 2nd paramete

Question

given the 1D signal data, I am asked to apply butterworth filter. it is mentioned that it has to be zero-phase digital filter, 2nd order and cutoff frequency = 10 Htz.

I have the following questions:

1. I understand zero-phase digital filtering. But does that mean while designing butterworth filter I should pass 'n' as 1? because forward and backword will make it 2.

2. We are NOT provided sampling frequency. Had it been provided, I would have used the following method:

   fs = 1000           % let us say
   fc = 10             % cutoff
   Wn = fc / (fs / 2)  
   [b, a] = butter(2, Wn) 
   

but fs is not provided. Then should I directly use 0.1 as 2nd parameter to butter function?

We are also provided with the time of the each data point in the signal. Is there a way to compute a sampling frequency from these times?

Your help is appreciated.

Answer 1

If you have time of the each data point in the signal, then there are two possibilities:

if time difference between points is constant, calculate sampling frequency from this difference

if time difference varies, find reliable mean value, build equidistant time grid using this value, and interpolate data into this grid