How to reduce the cut-off frquency of a digital filter?

Question

I have created a low pass Butterworth filter in python. What can be done so that I could reduce the cut off frequency to millihertz range? Is it possible even? Below is the code that I have used.

def butter_bandpass(cutoff_freq, fs, order=5):
   nyq = 0.5 * fs
   cutoff_freq = cutoff_freq / nyq
   b, a = butter(order, cutoff_freq, btype='low')
   w, h = freqz(b, a)
   return b, a

def butter_bandpass_filter(data, time, cutoff_freq, fs, flag, order=5):
   b, a = butter_bandpass(cutoff_freq, fs, order=order)
   #zi = lfilter_zi(b, a)
   y = lfilter(b, a, np.array(data))
   return y

Answer 1

If the cutoff frequency is too small a fraction of Fs, a 5th order filter will become numerically unstable (rounding "errors" will create NaNs). Try lowering the sample rate Fs by extreme downsampling of the data.