own code, loop form to vector form

hello, I have my own code to obtain the fft, a vector x that corresponds to a signal in time domain is entered, and the fft returns me, this function uses loops, I need to have the same function but without loops, that is, transforming the iterators of the loops in vectors or matrices.I have tried in various ways but I have not succeeded. somebody could help me?

the code is the following:

this fft code is from radix 2 method.

function [ y ] = my_fft_for( x )   

N1 = length(x);                             % calculates the size of the Xn sequence

nFFT = 2^ceil(log2(N1));                    % calculates the number of samples to complete
x =[x zeros(1,nFFT-N1)];                    % The sequence is completed with 0's to nFFT elements
 
N=length(x);                                % calculates the number of samples of xn
b=bin2dec(fliplr(dec2bin (0:1:nFFT-1)))+1;  % Reordering of samples (reverse bit)
x=x(b);                                     % Signal reordered
                                                                 
S=log2(N);                                  % calculates the number of stages
Half=1;                                     % Initialize with half value
for stage=1:S                               % FOR loop of stages of the algorithm Log2 (N)
    for index=0:(2^stage):(N-1)             % Butterflies for each stage of the algorithm
        for n=0:(Half-1)                    % A butterfly is calculated and the result is saved
            pos=n+index+1;                  % Index of samples
            pow=(2^(S-stage))*n;            % Power of complex multiplication
            w=exp((-1i)*(2*pi)*pow/N);      % Complex multiplication
            a=x(pos)+x(pos+Half).*w;        % First part of the butterfly
            b=x(pos)-x(pos+Half).*w;        % Second part of the butterfly
            x(pos)=a;                       % Saving result of the first part of the butterfly
            x(pos+Half)=b;                  % Saving result of the second part of the butterfly
        end
    end
Half=2*Half;                                % Calculating the next "Half" value
end
y=x;                                        % The result of the function is saved
end

and i have this test:

clc, close all, clear all
 
%% SIGNAL CONSTRUCTION
% Signal duration
duration = 1;
% First frequency component
f1 = 10;
% Second frequency component
f2 = 20;
% Sampling frequency
Fs = 10*f2;
% Sampling period
Ts = 1/Fs;
% Vector of times
t = 0:Ts:duration;
% Signal construction
% Original signal without (10) + without (20)
xn = sin(2*pi*f1*t) + sin(2*pi*f2*t);
% N1 = length (xn);% The size of the sequence Xn is calculated
% FREQUENCY DOMAIN
% Number of signal samples
N = length (xn);
    
% Calculation of the value that is the closest multiple of 2 and multiplied by a
% factor to increase the number of samples and have a better result
nFFT = 2 ^ (ceil(log2(N)));
 
% Xn2 = my_fft_vectorial (xn);
% I apply the matlab FFT function
Xn1 = my_fft_for (xn);
 
% The module of the complexes called PERIODOGRAM is calculated
Periodogram = abs (Xn1);
 
% Calculation of the AXIS of frequencies: same number of points as PERIODOGRAM and that are between 0 and Fs:
f = linspace (0, Fs, nFFT);
 
% With the two axes ready, we just graph:
plot (f, Periodogram);

% Due to mid-period symmetry, we are only interested in visualizing half of the PERIDODOGRAM:
axis ([0 Fs/2 0 max(Periodogram)])
xlabel ('F (Hz)')
title ('PERIODOGRAM based on Matlab FFT')

Note:

i need transform from loop form to vector form is similar to this:

DFT loop form

DFT transform to vectorial form

HELP PLEASE!

Answer 1

[Salman Ahmed]

Hi Stalin,

I assume you need to vectorize all the loops in your code. You could refer to a possible workaround here that reduces two of the loops in your code. It is difficult to reduce the third loop without re-writing the logic as index and pos variables change size iteration to iteration. Hope it helps.

function [ y ] = my_fft_for( x )   
N1 = length(x);                             % calculates the size of the Xn sequence
nFFT = 2^ceil(log2(N1));                    % calculates the number of samples to complete
x =[x zeros(1,nFFT-N1)];                    % The sequence is completed with 0's to nFFT elements
 
N=length(x);                                % calculates the number of samples of xn
b=bin2dec(fliplr(dec2bin (0:1:nFFT-1)))+1;  % Reordering of samples (reverse bit)
x=x(b);                                     % Signal reordered
                                                                 
S=log2(N);                                  % calculates the number of stages
Half=1; 

for stage=1:S                               % FOR loop of stages of the algorithm Log2 (N)
            index=0:(2^stage):(N-1);        % Butterflies for each stage of the algorithm
            n=0:(Half-1);                   % A butterfly is calculated and the result is saved
            pos=n+index'+1;                 % Index of samples
            pow=(2^(S-stage)).*n;           % Power of complex multiplication
            w=exp((-1i)*(2*pi).*pow/N);     % Complex multiplication
            a=x(pos)+x(pos+Half).*w;        % First part of the butterfly
            b=x(pos)-x(pos+Half).*w;        % Second part of the butterfly
            x(pos)=a;                       % Saving result of the first part of the butterfly
            x(pos+Half)=b;                  % Saving result of the second part of the butterfly
            Half=2*Half; 
end                                         % Calculating the next "Half" value
y=x;  
% The result of the function is saved
end

[Stalin García Ruano]

thanks man, the code works perfect!!