I'm using a very simple 1st order Butterworth Filter shown in Matlab code:
order = 1;
cutOff = 0.1;
[b, a] = butter(order, (2*cutOff)/SampleRate, 'high');
So from the Matlab documentation of butter
, it is not hard to know the transfer function is:
$$H(z) = \frac{b_1 + b_2z^{-1}}{a_1 + a_2z^{-1}}$$
The question is, if I have a signal $x$ with variance $v$, after the signal $x$ is filtered by the above high-pass filter, what is the variance of the output signal? Will it change? How can I calculate it? And is the filter linear?