Can impulse response always be derived accurately if you know tranfer function numerically? and how to verify if it is the correct impulse response.

Assume H(f)=exp(j15e10/f) then since there is no well known pair have to find it numerically and can do this using matlab.

Fs=2e9; dF=2^10; f = (-Fs/2:dF:Fs/2-dF); H=exp(1i*15e10./f);

FR_data=H; IR_data=(ifft(ifftshift(FR_data))); h=IR_data;

figure; stem(real(h));

figure; plot(real(h));

Question is how would I verify if this is indeed the correct impulse response? Thank you.