Vectors problem

Hey Guys !!

I am working with vectors and I read about it before I post my question but can't still get it... Sorry if it is too basic but its difficult for me.. I have four vectors each of size 1x100.. x,y,g,z.. I did plot (x,y) and (g,z) and It is what I expect.. the four vectors are generated randomly so there is low chance the points values will be identical.. I want my first plot to be identical to my second but with leaving the first 3 points, to clear this part I mean usually points starts from point(1,1),(1,2),(1,3) etc but I shall leave those 3 points for the plot(x,y) and start from(1,4) and make it identical to the first point in plot (g,z) so x,y(1,4)= g,z(1,1) and so on.. so basically the two plots are now identical but the first is a shifted version.. I start breaking the steps to achieve this 1. since the vectors are separated in matlab workspace I thought first I need to concatenate the vectors together.. so I created A[x;y] 2x100 and B[g,z] 2x100.(Successful, I did that) 2. I looped through the points in B with ignoring the first 3 points of A and starting from(1,4) and copy the points.. first 3 points set it as NaN(Successful, I did that) 3.I need now to plot my vectors A,B first in two different plots then in same plot to see the result, here is my problem.. I thought by doing the first two steps I can easily plot A and B scale one down then I will be able to see that they the same but one is shifted but that didn't happen..

Is the way I broke down the problem wrong or my last step was not done properly???

Thanks all in advance !!!

Answer 1

[Javier]

See this and check if it's you're looking for:

function princ

lambdaMax=45;
T=50;
x=-2*pi:1/5:2*pi;

lambda =@(x)( sin(x)*(20+30));  
S = Trial(lambdaMax,lambda,T)
hold on  
% plot(S,lambda(S))

X = linspace(min(S),max(S),100);  
Y = pchip(S,lambda(S),X);
Signal1=[X;Y]
plot(X,Y,'b')

lambdaFirst =@(x) (sin(x-4)*(20+30)); 
S1 = Trial(lambdaMax,lambdaFirst,T);
% plot(S1,lambdaFirst(S1))
X1 = linspace(min(S1),max(S1),100);  
Y1 = pchip(S1,lambdaFirst(S1),X1);
Signal2 = [X1;Y1];
plot(X1,Y1,'r')%phase shitf
plot([zeros(1,4) X(1:end-4)],Y1,'black')%delay shift

% Signal1(1,1)= NaN;
% Signal1(1,2)=NaN;
% Signal1(1,3)=NaN;
% Signal1(1,4)=NaN;
% d = 4;
%    for i=1:100-d
%      Signal1(:,i+4) = Signal2(:,i);
%    end

xlabel('t')
ylabel ('cos(x)')
legend('Original','Phase shift','Delay shift')
hold off;
end
function S = Trial(lambdaMax,lambda,T)
t = 0;
I = 0;
S = [];
u = rand;
t = t - log(u)/lambdaMax;
while t <= T
    u=rand;
    if (u < lambda(t)/lambdaMax)
        I = I+1;
        S(I) = t;
    end
    u = rand;
    t = t - log(u)/lambdaMax;
end
end

[Susan]

It just plot the blue one no red plot??

[Javier]

the blue is the original and te red is the shifted one

[Susan]

and I can't see anything to do with the delay??? or even coping the content?

[Susan]

No red in the graph.. It only shows the blue?

[Javier]

close the figre and try again

[Javier]

Does it work?

[Javier]

I've change the code to show both delays phase and only shift

[Susan]

I can see it now but how can I scale it to bring it down and see if its working??? at the moment its drawn on top of eachother

[Javier]

Do you want to see them in diferent graphics?

[Susan]

No on the same graph but I want to scale one of them down a bit so It will be clear for me to see if they identical but one is shifted .. How can scale one of them down?

[Javier]

I think you can scals, you can zoom it/out in which are in the sidebar

[Susan]

There is a way to scale it in Matlab using axis([Xmin Xmax Ymin Ymax]); but tried different values and can't seem to do it properly but I believe this is what I should use !

[Javier]

Add this after hold off,line 33

figure(2);hold on;

subplot(3,1,1);plot(X,Y,'b');

subplot(3,1,2);plot(X1,Y1,'r')%phase shitf

subplot(3,1,3);plot([zeros(1,4) X(1:end-4)],Y1,'black')%delay shift

hold off;

[Javier]

Forgot the legend:

figure(2);hold on;

subplot(3,1,1);plot(X,Y,'b');xlabel('t');ylabel ('cos(x)');legend('Original')

subplot(3,1,2);plot(X1,Y1,'r');legend('Phase shift');xlabel('t');ylabel ('cos(x)');%phase shitf

subplot(3,1,3);plot([zeros(1,4) X(1:end-4)],Y1,'black');xlabel('t');ylabel ('cos(x)');legend('Delay shift')%delay shift

hold off;

[Susan]

Can you please explain to me how you shift it and how you made both signals identical?.. I don't know how to test it but If you explain to me I will try it with different data?? figure(2);hold on;

subplot(3,1,1);plot(X,Y,'b');

subplot(3,1,2);plot(X1,Y1,'r')%phase shitf

subplot(3,1,3);plot([zeros(1,4) X(1:end-4)],Y1,'black')%delay shift

hold off;

[Susan]

and what is the difference between phase shift and delay shift?? I will be thankful if you just explain to me what you exactly did and how you achieved it !!

Answer 2

[Javier]

I cannot understand well the problem,do you want to shift the first three elements of each vector?

[Susan]

I did the shifting of the content of the vector but now I want to plot it and see the actually the both identical but one is shifted? I went through the steps I described above but the plotting seems issue since instead of x,y which are separate vectors I used A[x;y] because I need the pair of value to do the shifting.. Do you understand my problem now?

[Susan]

What to do you mean? Can you explain it a bit more,please?

Answer 3

[Paulo Silva]

%generate data to work with
t=linspace(0,10,10); %time vector
v=rand(1,numel(t));  %vector with some random values
cla;hold on
plot(t,v)
n=3; %number of elements you want to remove from v 
v=[v(n+1:end) nan(1,n)]; %remove the first n elements
%and put the same n number of NaN in the end of v
%so that the vectors remain with the same size
plot(t,v,'r')
legend('signal','signal shifted')

[Susan]

Your code worked when I run it but could not apply it to mine?.. I posted my code to be able to see which ones are my vectors and to see the steps I made to solve this problem !!

[Paulo Silva]

What my code does is what you asked in: 'I want my first plot to be identical to my second but with leaving the first 3 points, to clear this part I mean usually points starts from point(1,1),(1,2),(1,3) etc but I shall leave those 3 points for the plot(x,y) and start from(1,4)'

[Susan]

Yeah I know but my v is a lmbda(S) Function..I did this but just a blank graph i got.. cla;hold on

plot(t,Signal1)

n=3;

Signal1=[Signal1(n+1:end) nan(1,n)];

plot(t,Signal1,'r')

legend('signal','signal shifted')

[Susan]

Its Signal1 where I get the pair values (x,y) Signal1 is 2x100 vector

[Paulo Silva]

n=3; %shift Signal1 n columns

Signal1(1,:)=[Signal1(1,n+1:end) nan(1,n)];

Signal1(2,:)=[Signal1(2,n+1:end) nan(1,n)];

[Susan]

I tried it still the graph is blank!!

Answer 4

[Javier]

Well you has done a lot of question, I'll try to explain:

1ªwhat is the difference between phase shift and delay shift, phase shitf:is when you change the phase in a sine or cosine fase, e.g. sin(x)->hasn't got a gap in the phase

sin(x+-phi)->here, phi is a phase gap, due to you're adding or subtract the value phi, see this link http://en.wikipedia.org/wiki/Phase_(waves)#Phase_shift On the other hand, a delay in the singal means that the signal starts after a quatum of time, in your case 4seconds or samples depending on the units you are working with, the diference between this and the phase shift, is that all the signal is moved or shifted 4seconds/samples.

2ª Here,I've not done anything that you haven't done before, only I have plotted the ordinate of signal1 ,Y, on the abscissa of signal X, and with 'b' I command matlab to plot in blue

    In this code:
    lambda =@(x)( sin(x)*(20+30));  
    S = Trial(lambdaMax,lambda,T)
    hold on  
    % plot(S,lambda(S))
    X = linspace(min(S),max(S),100);  
    Y = pchip(S,lambda(S),X);
    Signal1=[X;Y]
    plot(X,Y,'b')

3ªIn this case,I have imposed the phase shift in the signal, notice that if I had set sin(x+4)*(20+30), the shitf will be to the left. Then I used this variable with your code and lastly with the new axe values(X1,Y2) plot again,here I have not to touch the 'x' axe because I have modified it in the sine expression,so it isn't necessary do it again. With 'r' command matlab to plot in red the singal.

    lambdaFirst =@(x) (sin(x-4)*(20+30)); 
    S1 = Trial(lambdaMax,lambdaFirst,T);
    % plot(S1,lambdaFirst(S1))
    X1 = linspace(min(S1),max(S1),100);  
    Y1 = pchip(S1,lambdaFirst(S1),X1);
    Signal2 = [X1;Y1];
    plot(X1,Y1,'r')%phase shitf

4ªThe delay of the signal is done with the command below,as you can imagine before 4s(I'm going to asume time units) there is not delay signal due to the fact that it hasn't arrived yet, so the values of x axe should be zero, for that I use the command "zeros(n,m)" which set a matrix of nxm zeros elements.After this 4seconds there is singal, so I'have copied the values of the x-axe Singal1 given that we want to be the same in signal2, so as to do this I copy the values of X, but realizing that if we want to draw with plot, the vector must have the same length, so I have to subtract the 4 last values of the X axe and that is done with "X(1:end-4)", I'm telling matlab to take the values of X from 1 to last value less the 4 last. Finally we have to get together the first four values of x(which ones were zero) and the rest, and that we make with the "[ ]", this way our x axe will be:

xDelay=[zeros(1,4) X(1:end-4)];
plot(xDelay,Y1,'black')%delay shift

or in one sole command as I've used:

plot([zeros(1,4) X(1:end-4)],Y1,'black')%delay shift

I suggest that you read the documentation of "plot" to have a clear idea of this command, you can do that by typing "help plot" on matlab prompt

Regards

[Susan]

Yeah your right, I pretty much did it, it was the plot causing me trouble.. I always do the main and end up sorting out something that should be easy but will definitely read the documentation regarding the plot.. Thanks a lot for your time and effort.. Really appreciate it :)

Answer 5

[Javier]

So you want to do something like this:

xy=[ 1;1
     2;2
     3;3
     4;4 
     5;5
     6;6 
     7;7]
gz=[ 8;8
     9;9
     10;10
     11;11
     12;12
     13;13
     14;14]
You make the shift and gets something like:
xy=[ 1;1
     2;2
     3;3
     4;4 
     8;8
     9;9 
     10;10
     ...]
gz=[ 8;8
     9;9
     10;10
     11;11
     12;12
     13;13
     14;14]

and now what do you want to plot?

[Susan]

I explained below with my code.. I am too confused !!

Answer 6

[Susan]

I am well confused to be honest, I think the way I broke down the problem is logical but still can't figure out how to plot it. @Javier I don't get what you trying to do, @Paulo your small piece of code worked when I run it and was positive I will be able to make it work in mine but It didn't happen :( !! I will post my code so You can see what exactly I am talking about!!! Trial simply generates the random numbers and the Script is below to run it..

function S = Trial(lambdaMax,lambda,T)
t = 0;
I = 0;
S = [];
 u = rand;
t = t - log(u)/lambdaMax;
 while t <= T
         u=rand;
    if (u < lambda(t)/lambdaMax)
        I = I+1;
        S(I) = t;
    end
    u = rand;
    t = t - log(u)/lambdaMax;
end

lambdaMax=45;
T=50;
  x=-2*pi:1/5:2*pi;
lambda =@(x)( sin(x)*(20+30));  
S = nonhomogeneousPossion(lambdaMax,lambda,T)
hold on  
plot(S,lambda(S))
%plot(S,lambda(S))
xlabel('t')
ylabel ('cos(x)')
X = linspace(min(S),max(S),100);  
Y = pchip(S,lambda(S),X);
Signal1=[X;Y]
plot(X,Y)

lambdaMa = 45;
T=50;
x=-2*pi:1/5:2*pi;
lambdaFirst =@(x) (sin(x)*20+30); 
S1 = nonhomogeneousP(lambdaMa,lambdaFirst,T);
plot(S1,lambdaFirst(S1))
xlabel('t')
ylabel ('cos(x)')
X1 = linspace(min(S1),max(S1),100);  
Y1 = pchip(S1,lambdaFirst(S1),X);
Signal2 = [X1;Y1];

Signal1(1,1)= NaN;
Signal1(1,2)=NaN;
Signal1(1,3)=NaN;
Signal1(1,4)=NaN;

d = 4;
   for i=1:100-d
     Signal1(:,i+4) = Signal2(:,i);
   end

[Javier]

I still don't understand what do you want to plot, sorry :(

[Susan]

Generally speaking I am trying to plot a signal and another one(this one should be identical to the first one but shifted) then plot them both on the same graph scale it (to see that the both are same signals but one is shifted).. In my code to achieve this I created Signal1[x;y] and signal2[X1,y1].. I shifted the content of Signal2 to Signal1 its the loop there and made the first 4 entries NaN so I will ignore them.. NOW I want to plot both signals scale it to see that they are actually same exact signal but one is shifted !!!

[Javier]

ok! Now I understand!

[Susan]

Any Idea?

[Javier]

Is sin(x)*(20+30) the original singal?

[Susan]

Yeah, thats the original signal I pass it into the function lambda!!

And see X,Y.. when I plot it plot(X,Y) thats what i want to have as the original then create a shifted one !

[Susan]

If you see it its pass to lambda so I will get the values and then store it into S.. then seee X and Y .. Hope its clear now !!

[Javier]

And you want a delay in the singal shifted or a phase change?

[Susan]

They should be identical but just a bit of delay and I thought by making the first 3 points NaN will do it.. If u see d=4 and the loop is shifting the content of the second signal into the first signal starting from Signal(1,4)=Signal(1,1)... Do you have an idea how to achieve this by looking what I am doing in my code ?? I am too confused about this???

[Susan]

So eventually I should have the first signal plotted and the second one(Its identical coz I copied all its content to the first starting from (1,4))plotted underneath and It will be obvious that they are both identical but one is delayed a bit!!!