Frequency response of filter  signal mix
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
$$ H'(z) = a + (1-a) \cdot H(z) $$