If the action of L on complex exponentials is described by Equation (135a), and if G(−f) = G ∗ (f) for all f, what does L do to sines and cosines? Suppose that gp(·) and hp(·) are two periodic...

If the action of L on complex exponentials is described by Equation (135a), and if G(−f) = G ∗ (f) for all f, what does L do to sines and cosines?

Suppose that gp(·) and hp(·) are two periodic functions with period T such that

Let {Gn} and {Hn} be their Fourier coefficients as defined by If we regard hp(·) as a function of interest and gp(·)/T as a filter, their convolution

can be regarded as a filtered version of hp(·) (the above is Equation (96b)). What plays the role of the transfer function here?