Convolution of spectra to sensor response function?

I am really sorry if it is wrong place to ask this question but i couldn't not find any stackexchange website appropriate. i have some reflectance values of a material which are measured in 10.5 and 12.5 micrometers interval. This spectra is extracted from a spectral library. Then by using Kirchhoff's Radiation Law i calculated the emissivity values in each wavelength.

The problem is that, Here is the spectral response of Landsat5 TM thermal band. --> http://atmcorr.gsfc.nasa.gov/L5_handbook.rsp I have to convolve these emissivities to the spectral response above. Bu i dont have any idea. How can i do it?

I found the solution after searching in articles, Here is the convolution = $$e_{i} = \frac{\int_{\lambda =\lambda _{1}}^{\lambda _{2}}f_{i}\varepsilon \left ( \lambda \right )\partial\lambda }{\int_{\lambda =\lambda _{1}}^{\lambda _{2}}f_{i}\partial\lambda}$$ Where i = channel number, $\lambda$ is wavelength, $\varepsilon \left ( \lambda \right )$ spectral emissivity optained from spectral library, $f_{i}$ sensors spectral function and $e_{i}$ is channel emissivity that we want to find. $\lambda _{1}$ and $\lambda _{2}$ are upper and lower bounds of thermal band.