I have a filter where the input is:
$$ x(t) = s(t) + w(t) $$ which is signal plus white Gaussian noise and the output is $y(t)$. If the impulse response of the filter is $h(t)$, then:
$$y(t) = s(t)*h(t) + w(t)*h(t)$$
I have given the following equation to calculate the SNR:
$$SNR = \frac{\int_{-\infty}^\infty|s(t)*h(t)|^2 dt}{\int_{-\infty}^\infty|w(t)*h(t)|^2 dt}$$
And in frequency domain, following the Parseval's theorem:
$$SNR = \frac{\int_{-\infty}^\infty|S(f)H(f)|^2df}{\int_{-\infty}^\infty|W(f)H(t)|^2 df}$$
I wonder how this represents the signal power and noise power at numerator and denominator, respectively? Cause it is more like calculating energy than power.