# Interpolationg phase and magnitudes, Transformation function

I am trying to filter signal x(n), n = 150. I made a filter with few frequency points on the x axis , [-11., -9., -3., -2., -1., 1., 2., 3., 9., 11.]) I also defined linear magnitudes and phase in radian for corresponding frequencies. It would look as in the following: Frequency F, manitude H and phase in each column.

      ([[-11.    ,   3.1623,  -0.8203],
[ -9.    ,   5.0119,  -1.3614],
[ -3.    ,   2.5119,  -0.4014],
[ -2.    ,   3.9811,  -0.9599],
[ -1.    ,   1.5849,  -0.4363],
[  1.    ,   1.5849,   0.4363],
[  2.    ,   3.9811,   0.9599],
[  3.    ,   2.5119,   0.4014],
[  9.    ,   5.0119,   1.3614],
[ 11.    ,   3.1623,   0.8203]])


The sample rate of the signal is srate = 1000. One can obtain the frequency of the real signal by doing, f_sig = np.fft.fftshift(np.fft.fftfreq(n,1/srate)).

How do i obtain the Transformation function of the signal ?

H(sig) = |H|x exp (ixphi)

I suppose i need to interpolate magnitude and the phase, but don't know how?

Do you have any idea, how i may implement this?

Many Thanks.