I modulated signal using BPSK modulation and I have series of -1 and 1. Now I have to pass these signal from band limited channel that has frequency response of the form $$\frac{s^2}{as^5+bs^4+cs^3+ds^2+es+f}.$$ Now I am thinking to convolve my -1 and 1 with time domain version of the above frequency response. I defined $a$, $b$, $c$... as a symbolic variable and I have their numerical value however I need to have my impulse response in terms $a$, $b$, $c$... Therefore I would like to know:
How to find impulse response when the frequency response is order 5 in denominator? Matlab seems to give me error message when I leave the expression in terms of symbolic coefficients.
Is my reasoning correct to multiply square pulse shape with a carrier and then convolve it with the impulse response of the channel?
Also what do you think is a good way to demodulate the signal? would that be sufficient to multiply the received signal by my basis vector like cosine or sine?