We present a method to efficiently simulate the measurements of a broadband infrared instrument. The High Resolution Infrared Radiation Sounder (HIRS) instrument is used as example to illustrate the method. The method uses two basic ideas. Firstly, the channel radiance can be approximated by a weighted mean of the radiance at some representative frequencies, where the weights can be determined by linear regression. Secondly, a near-optimal set of representative frequencies can be found by simulated annealing. The paper does not only describe and analyze the method, it also describes how the method was used to derive optimized frequency grids for the HIRS instruments on the satellites TIROS N, NOAA 6-19, and Metop A. The grids and weights, as well as the optimization algorithm itself are openly available under a GNU public license. ; We present a method to efficiently simulate the measurements of a broadband infrared instrument. The High Resolution Infrared Radiation Sounder (HIRS) instrument is used as example to illustrate the method. The method uses two basic ideas. Firstly, the channel radiance can be approximated by a weighted mean of the radiance at some representative frequencies, where the weights can be determined by linear regression. Secondly, a near-optimal set of representative frequencies can be found by simulated annealing. The paper does not only describe and analyze the method, it also describes how the method was used to derive optimized frequency grids for the HIRS instruments on the satellites TIROS N, NOAA 6-19, and Metop A. The grids and weights, as well as the optimization algorithm itself are openly available under a GNU public license.