own code, loop form to vector form

조회 수: 2(최근 30일)
Stalin García Ruano
Stalin García Ruano 2021년 8월 15일
댓글: Stalin García Ruano 2021년 8월 31일
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!

채택된 답변

Salman Ahmed
Salman Ahmed 2021년 8월 30일
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
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Stalin García Ruano
Stalin García Ruano 2021년 8월 31일
thanks man, the code works perfect!!

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