On the use of Permutation matrix to perform iFFT
Y and Z should show the same values

clear;
%Create random vector x 
x = randn(32,8); 

%take ifft along each column 
y = ifft(x); 
Y = reshape(y,[],1);

z = reshape(x,[],1);   %
d=conj(dftmtx(32))/32;
X = kron(eye(8),d); 
Z = X*z;