Filters performance analysis I am working on some experimental data which, at some point, need to be time-integrated and then high-pass filtered (to remove low frequency disturbancies introduced by integration and unwanted DC component).

The aim of my work is not related to filtering, but still I would like to analyze more in detail the filters I am using to give some justification (for example to motivate why I chosed to use a 4th order filter instead of a higher/lower one).

This is the filter I am using:

delta_t = 1.53846e-04;
Fs = 1/delta_t;
cut_F = 8; 
Wn = cut_F/(Fs/2);
ftype = 'high';
[b,a] = butter(4,Wn,ftype);
filtered_signal = filtfilt(b,a,signal);


I already had a look here: https://stackoverflow.com/questions/5591278/high-pass-filtering-in-matlab to learn something about filters (I never had a course on signal processing) and I used 

fvtool(b,a)


to see the impulse response, step response ecc. of the filter I have used.

The problem is that I do not know how to "read" these plots.

What do I have to look for? 

How can I understand if a filter is good or not? (I do not have any specification about filter performances, I just know that the lowest frequency I can admit is 5 Hz)

What features of different filters are useful to be compared to motivate the choice? 

For example, what info can I see plotting the round-off noise power spectrum of 2 different filters?(high pass Butterworth of different orders: 4 and 22)


EDIT

I tried decimating the signal to reduce the sampling frequency as suggested in the comments and this is what I get



The green one is the new filter's round off noise spectrum having reduced the sampling frequency (now = 325 Hz), the blue one is the older with sampling frequency = 6.5 kHz.

Things look a bit better but still not good enough, am I right?
OK, doing a design of a Butterworth high pass filter with a cutoff frequency of 8Hz and a sampling frequency of 325Hz using scilab by:

 bw = iir(4,'hp','butt',[8/325 0.5],[0.1,0.1]);


then the filter is:

                                  2  
0.8168388 - 3.2673552z + 4.9010328z   
               3            4         
   - 3.2673552z + 0.8168388z          
------------------------------------  
                                   2  
0.6672256 - 2.9384352z + 4.8677204z   
               3   4                  
   - 3.5960396z + z                   


and the frequency response looks like:



So I'm not sure what you're doing for the design, but it doesn't appear to be high pass.

One thing that may help is if you could share what your data looks like (say 256 or so points?).