FFT analyzing of signal and signal reconstrution. (I want to reconstruct by suming a*sin(w*t-phi)

% I built a square wave simply by writing a file from 0-0.0128 for time and amplitude of 1 and -1. after analyzing with the fft %fuction. I want to reconstruct the Sqare wave by summing, not the IFFT function. The following code is how I did it. However, there %seems to be a missing cos(x) component. What am I missing?

figure(20)

plot(timesimple,simpleamp)

Simple=fft(simpleamp);

MagSimple=abs(Simple);

PhaseS=angle(Simple);

figure(21)

plot(MagSimple)

title('Square Wave FFT')

dsf=1/(.0001*64);

SimpFreq=(timesimple/.0001)*dsf;

ResultS=0;

for loop=1:64

    a=MagSimple(loop)/64;

    b=loop*78.1250;

    c=PhaseS(loop);

    ResultS=ResultS+a*sin(2*pi*b*timesimple+c);

end

figure(22) plot(ResultS)

Answer 1

[Daniel kiracofe]

You forgot the negative frequencies. You didn't state explicitly the definition of simpleamp, but I think length(Simple) should be 128. In this case loop need to run from 1:128, and SimpFreq should include both the positive and negative frequencies. You might look at fftshift().