how this function of idtft works

hey this program of mine computes inverse discrete time fourier transform but theorically i dont know how it works, can anybody help me ?

function x=idtft(w,X,n)
% x=IDTFT(w,X,n) computes the invrse discrete-time fourier transform of X.
% w is the independent variable in the frequency domain in radians.
% X is the spectrum X(e^jw)
% n is the time values at which the inverse transform is to be computed
%
% See also DTFT, CTFT, ICTFT
dw=w(2)-w(1);
    idx_2p=find((w>=min(w)) & (w<min(w)+2*pi));
    x=zeros(size(n));
    for i=1:length(n)
        x(i)= sum(X(idx_2p).*exp(1j*w(idx_2p)*n(i))*dw)/2/pi;
    end

Answer 1

[Hassaan]

Theoretical explanation:

1. w (Frequency Domain Samples): These are the frequency domain sample points where the spectrum X is defined, typically in radians.
2. X (Spectrum): This is the frequency domain representation (spectrum) of your signal, denoted as X(e^jw).
3. n (Time Samples): The time points at which you want to compute the inverse transform.
4. dw (Frequency Step): This represents the difference in frequency between adjacent points in w. It is used to approximate the integral in the inverse transform.
5. Inverse Transformation Process: The code sums over the frequency components (X(idx_2p).*exp(1j*w(idx_2p)*n(i))) scaled by dw and normalizes by 2*pi. This sum effectively approximates the integral required in the inverse Fourier transform.
6. Loop Over Time Samples: The for loop calculates the inverse transform value for each time sample in n.

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