Digital filter design of time series for specified frequency response function
This is the classical problem of filter design: 


  You've got a frequency response that you want, how to implement it using a FIR?


I'm not going to lay out all the theory here, because it can easily be found by looking for Fourier approximation methods for FIR design or windowing methods, but the idea is easy enough:


Take your frequency response. Sample it at many points.
Take the inverse FT. You get something long, which, when convolved with a signal, would have the sampled frequency response (because of the convolution theory of the Fourier Transform).
Because the result is a very long filter and exhibits undesirable fringe behaviour, apply a window function to cut off some of the coefficients. The result is your filter taps.


There's iterative methods of increasing the match between desired and actual response given a limited amount of freedom by a limited number of taps; but this would exceed the scope of the question.