The impulse response of an LTI system is aperiodic and I pass in a periodic signal. Now I need to find the Fourier series representation of the output.

Since Convolution in time domain is multiplication in frequency domain, I think that converting both signals in their respective frequency domain and multiplying them would work.

Therefore, finding the Fourier series of first and transform for second. Is it a correct way?

My question being is it legal to multiply fourier series and transform the way I'm doing?