repmat() introduces an unnecessary phase shift

Hi, I used repmat command to create a periodic waveform.

However I noticed repmat() introduces a phase shift of one element in the array in each repetition.

I compared the analytical waveform (plotted in Green) with the repmat generated signal

Pls give some advice to correct.

Screen Shot of the plot: http://imgur.com/rR3SEyP

Code:

clc;
clear all;

fc=4; %control waveform

T=1/fc;

t1=0:.001:T/6;
t2=T/6:.001:2*T/6;
t3=2*T/6:.001:3*T/6;
t4=3*T/6:.001:4*T/6;
t5=4*T/6:.001:5*T/6;
t6=5*T/6:.001:6*T/6;

%Positive limit
Ap=sqrt(3) + sin(2*pi*t1*fc - 2*pi/3);
Bp=sin(2*pi*t2*fc);
Cp=sqrt(3) + sin(2*pi*t3*fc + 2*pi/3);
Dp=sin(2*pi*t4*fc - 2*pi/3);
Ep=sqrt(3) + sin(2*pi*t5*fc + 2*pi);
Fp=sin(2*pi*t6*fc + 2*pi/3);

%Negative Limit
An=sin(2*pi*t1*fc - 2*pi/3);
Bn=-sqrt(3) + sin(2*pi*t2*fc);
Cn=sin(2*pi*t3*fc + 2*pi/3  );
Dn=-sqrt(3) + sin(2*pi*t4*fc  + 4*pi/3);
En=sin(2*pi*t5*fc );
Fn=-sqrt(3) + sin(2*pi*t6*fc + 2*pi/3);

t=[t1 t2 t3 t4 t5 t6];
yp=[Ap,Bp,Cp,Dp,Ep,Fp];
yn=[An,Bn,Cn,Dn,En,Fn];

%plot(t,yp,t,yn)

m=3 ; % Repetition 
n=numel(t);
tt=0:0.001:n*m*0.001-0.001;
yy_p=repmat(yp,1,m);
yy_n=repmat(yn,1,m);
max_shoothru=[yy_p;yy_n];

% analytical wave
 Y1p=((1-0.5*sqrt(3)))*sin(3*4*2*pi*tt +pi) + sqrt(3)/2;
 Y1n=((1-0.5*sqrt(3)))*sin(3*4*2*pi*tt +pi ) - sqrt(3)/2;
 analytical=[Y1p;Y1n];

%3 phase voltage waveforms
A_ph=sin(2*pi*tt*fc);B_ph=sin((2*pi*tt*fc)+ 2*pi/3);C_ph=sin((2*pi*tt*fc)- 2*pi/3);
waves=[A_ph;B_ph;C_ph];

plot(tt,max_shoothru,tt,waves,'r',tt,analytical,'g'); 
grid on;

Answer 1

[Walter Roberson]

Suppose you create a periodic waveform over 0 to 1. Then when you repmat it, you get [0...1 0...1 0...1]. Note that the second 1 is not at the position that would correspond to 2, and is instead one sample later.

To correct this, what you need to repeat is the samples over 0 to 1 without the 1 itself. e.g.,

   W = linspace(0, 1, 1000);
   W25 = repmat(W(1:end-1), 1, 25);

If you want a final return to beginning you can,

   W25 = [repmat(W(1:end-1), 1, 25), W(end)];