Convolve a SED with a filter. Is convoluting the mathematical operation?
To get the flux of an SED through a particular filter, you actually multiply the the SED by the filter's response. Talking about convolution in this context is a bit of a misnomer. 

Basically, for each wavelength, you look at what fraction of the light will go through the filter, and you sum up the values you get at those wavelengths. 
The division by $\int T_{b}(\lambda)d\lambda$ is just a normalization term.