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I would like to do an inversion of fourier transform for my function y(iw) at some value real value z. I am confused at how to specify my function y(iw) and z in MATLAB's IFFT(X).

In the continuous setting, the inverse fourier transform, ift(), would be

ift(z) = 1/2pi * Integral [ e^(-iwz) y(iw) dw ]

In other words, I specify z and specify y, which is only a function of w which I am integrating over. But how do I do this using MATLAB's IFFT, when it only takes an input X...

Does anyone have any recommendations of computationally solving these integrals for vectors of z and known analytical expression of y(iw)?