MATLAB fir2 - npt and lap

Question

This might not be the right place to ask this, but I'm hoping someone can explain two of the arguments in the MATLAB fir2 function. It is a function for designing filters using the frequency sampling method. There are two optional arguments:

npt - Number of grid points, specified as a positive integer scalar. npt must be larger than one-half the filter order: npt > n/2.

lap - Length of region around duplicate frequency points, specified as a positive integer scalar.

I am struggling to find any meaningful literature around this so if anyone could explain these two in further detail or point me to something to read that would be greatly appreciated.

Answer 1

npt is the number of frequency points that are used to define the desired frequency response. It's the length of the inverse FFT that is applied to the frequency domain data. It defaults to $512$ points, but if you want to design very long filters (with many taps) then you should choose a larger number.

lap defines the width of the transition band, if there is one. There is a transition band if there are two equal frequencies specified in the vector f, where a step in the desired response occurs. The wider the transition band the smaller the approximation error in the pass bands and stop bands, so there is a trade-off between steep transitions and approximation errors in the pass bands and stop bands.