I have a power spectral density function that has a mean square value of 64.
Given that the mean square is defined as the integral of the power spectral density, $$E[X^2]=\int\limits_{-\infty}^\infty{ G_X(f)\ df}$$ Substituting for mean-square value, $$64=\int\limits_{-\infty}^\infty{ G_X(f)\ df}$$ If the frequency (f) was scaled by 10, how would that affect the output and what are the algebraic steps taken to reach that answer?
Let f = 10f, $$64=\int\limits_{-\infty}^\infty{ G_X(10f)\ d(10f)}$$ I know dividing both sides by 10 would give me the right answer but what is the logic and steps behind this to make it valid?