# Correctly interpret Butterworth filter frequencies

I am using the butter function from the signal package in R to filter my data.

The data is Fourier-transformed (complex numbers) - and I want to filter out specific frequencies (I have a 256Hz sampling frequency, hence a 128Hz spectrum and say I want to filter only data from 4-8Hz).

I find conflicting documentation on what the correct values for W in this function should be:

butter(n, W, type = c("low", "high", "stop", "pass"), plane = c("z", "s"), ...) should they be 4/256 and 8/256? I find it hard to interpret whether my results with 4/256 and 8/256 are correct.

strength <- ftdata
low <- 4
high <- 8
bf <- butter(5, low/256, type="high")
bfsig <- filter(bf, strength)
bf <- butter(5, high/256, type="low")
bfsig <- filter(bf, bfsig)

plot(f,bfsig, type='l')

# Where ftdata is just the output from my Fourier transform. The 5 is the order of the filter.


I just want to know whether the "/256" makes sense here - or should it be 128 because of Nyquist frequency F/2?

EDIT:

Also, any idea why the below does not return the same result as the above?

 filt <- butter(5,c(low/256,high/256), "pass")
bfsig <- filter(filt, strength)


It should just be a combination of the low and high-pass filters.