How to implement IDFT using the positive frequencies of DFT, modulation and resampling on MATLAB?
Here is the IDFT with normal and positive only frequencies if it helps:

N=4;
A=rand(N-1,1) + j*rand(N-1,1);   % Random positive carrier
X=[0; A; 0; flipud(conj(A))];    % Hermitian symmetric DFT vector
Xp=[0; 2*A; 0; zeros(size(A))];  % Positive freq only DFT vector

x = ifft(X);         % Normal IDFT
xa = ifft(Xp);       % Analytic signal
xp = real(ifft(Xp)); % Same as normal IDFT