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ifft one side spectrum to get a real signal

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Dear Matlab Profession,
Please find the following code.
I have a code to generate a one side spectrum in frequency domain, I am not sure it is postive frequency or negative frequency.
But I do know the energetic portion of signal in time domain aftfter ifft must starts after 3.33 sec as either Figure (1) or (2).
The issue is based on Fourier transform theory, I should get a "real" signal, but I still get a complex signal in time domain.
May I ask how to fix it or use ifftshift? Thank you!
clear;clc;close all;
%% This is the time and frequency steps used to generate signals
sig_end=7; % in sec, r/cw=5000/1500=3.33 sec arrival already covered
Fs=400; % Sampling Freq, Fs/2 is the folding freq
dt=1/Fs; % Time Step
L=Fs*sig_end; % Signal Length: Fs* a number
t=(0:L-1)*dt; % physical time (s)
df=Fs/L; % frequency step
freq=0:df:Fs/2; %desired frequencies for broadband
%% Load one side spectrum generated from software
load('Sign_spectrum_one_side.mat','Pr')
Pr_other_side=conj(Pr);
Pr_two_sides_1=cat(1,Pr_other_side(2:end-1),flip(Pr));
Pr_two_sides_2=cat(1,Pr_other_side,flip(Pr(2:end-1)));
pr_two_sides_1=ifft(Pr_two_sides_1);
pr_two_sides_2=ifft(Pr_two_sides_2);
figure(1)
plot(t,pr_two_sides_1);
xlabel('Time (sec)');ylabel('Arbitrary magnitude')
figure(2)
plot(t,pr_two_sides_2)
xlabel('Time (sec)');ylabel('Arbitrary magnitude')

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Accepted Answer

Samatha Aleti
Samatha Aleti on 16 Oct 2019
ifft” of that vectors which have symmetric complex conjugate structure will result in real values.
Also, you may specify the "symflag" as symmetric while computing fft inorder to ensure that the output is real. Refer the following document for more information:
Refer the following link for detailed explanation:

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