Frequency response of filter  signal mix This might be a weird question but here's the setup: I have a few biquads that filter a signal $x[n]$ and output the filtered signal $y[n]$. I can calculate the frequency response of those biquads with the z-transform. Now I mix $x[n]$ and the filtered signal $y[n]$ such that the mixed signal $y'[n]= a \cdot x[n] + (1 - a) \cdot y[n]$ where $0\leq a\leq 1$. How would I go about calculating the frequency response of $y'[n]$?
The Z transform is linear. So if 
$$ Y(z) = H(z) \cdot X(z) $$ then
$$ Y^{'}(z) = a \cdot X(z) + (1-a) \cdot Y(z) = a \cdot X(z) + (1-a) \cdot H(z) \cdot X(z) = (a + (1-a) \cdot H(z)) \cdot X(z) $$ 

Hence
$$ H'(z) = a + (1-a) \cdot H(z) $$