I am modelling flow in a tube. I have the functions A(t) and Q(t), corresponding to the area and flow, respectively, where the tube is compliant and can change its cross-sectional area. I can calculate the flow velocity V(t) by V(t) = Q(t)/A(t);
I know that in the frequency domain, if I take the FFT of Q(t) I get F(Q(t)) = Q(w). Similarly F(A(t)) = F(w), and F(V(t)) = V(w).
I also know that Q(w) = conv(A(w),V(w)) where conv is the convolution integral. I was wondering are there any cases where I can approximate the convolution as Q(w)~A(w)*V(w)?
I am trying to come up with an approximate analytical solution in the frequency domain and such assumption would greatly simplify things. Are there any cases where this approximation could be close to be valid?