Highpass filter applied to noise Suppose the input signal is represented as $$y=x+w$$ where $x$ is the signal to be estimated and $w$ is AWGN. I design a high pass filter $H$. What does $$H^{T}Hw$$ represent? Will it be just AWGN but attenuated or will it AWGN completely distorted. We can also assume that $\sigma_w = 0.2$
The formula represents noise component of the output signal. AWGN stands for additive white gaussian noise, than after passing through the filter the noise will still be additive and gaussian but NOT white.