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I'm asked to design FIR filter, an ideal low pass filter.

I'm given with pass band frequency (wp) and stop band frequency (ws). Now, I have to choose Ns points from stop band and Np points from pass band. Taking the inverse will give me impulse response.

The problem is, Ns points are equally spaced and Np points are equally spaced. But the spacing of the points in pass band and stop band differ. How do I find the filter coefficients?

Thank you.

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It is not a good idea to have Np and Ns as constraints, for the exact reason you mention- it will usually cause unequal spacing. Instead, make N, the total number of points, a constraint, and then you will have the equal spacing that you need.

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