Remove unknown DC Offset from a non-periodic discrete time signal

Question

Is there some process that can determine / remove an unknown DC offset from a non-periodic discrete time signal?

The signal in in question has a sample rate of 25Hz and has harmonics of interest between 0.25 and 3 Hz.

I have tried using highpass filters mixed results, first I used a 10th order guassian with Fc = 0Hz, this did a good job of removing the offset but it severly attenuated the AC aswell although it did leave the signal shape intact, next I used a 168th order equilripple with a stopband at 0Hz and passband at 0.25Hz, the phase shift was too severe and the signal shape too distorted, the distortion could probably be reduced if the pass-band was brought down to 0.1Hz but this would just further increase the phase shift which I need to keep to the very minimum.

Before and after applying x - LPF(x), as suggested by Paul R

Answer 1

I recommend using a notch filter at DC and using filtfilt to make it zero phase.

a = [1 , -0.98]; b = [1,-1];

y = filtfilt(b,a,x);

The closer the second value of a gets to -1 the narrower your notch will be.

Answer 2

A DC offset means that some constant value was added to the signal (the name originates from adding a DC voltage to an analog AC signal). If the DC component is really constant (and not changing really slowly), then you don't have to design some high-order (and potentially unstable) high-pass filters - you can just subtract the average of your signal from the signal - which is, of course, a high-pass filter as well (averaging is a type of a low-pass, and '1 minus the average' is high-apss) --- but a very simple one.

If, on the other hand, you have a reason to believe that the DC component is not really a DC, but rather an AC with very low frequency, then you'd better average segments of your signal and not the signal as a whole, which is the same as using a low-pass filter with impulse response which is shorter then the length of the signal. In this case you have to make some assumptions about the "DC" component.