Inverse Fourier Transformation with a function in the exponent

I have a signal x[n] with it's Fourier Transform X[k]. I want a frequency-warped signal (x_warp[n]) by taking the inverse Fourier of X[k], with a warping function fun. I know the fun will be somehow incorporated to the exponent of original inverse Fourier e^(j*2*pi*k*n/N)

So far, I have the following code:

x_hat = 1/N * X(1:N/2+1) * exp(1j*fun'/Fs*2*pi*(0:N-1))
x_warp = 2*real(x_hat)

Fs=Sampling frequency. Could you please tell me if the expression in the exponent is correct or not? I.E. what will be exp(???) in the above code?

Thanks in advance!