Wiener Filter

Viewing 8 posts - 1 through 8 (of 8 total)
  • Author
    Posts
  • 06/16/2016 at 6:42 AM #9437 quote
    Renato Di Lorenzo
    Participant
    Average

    Hi.

    Is somebody able to write the code for the optimum Wiener filter?

    Best.

    Renato

    06/16/2016 at 8:47 AM #9440 quote
    Nicolas
    Keymaster
    Master

    Hello Renato,

    Why not, I just googled it and didn’t find any other trading platform formula that could be easily converted.

    Are you able to tell us more details about it and how you’d like it to operate on market price? Thanks.

    06/16/2016 at 10:47 AM #9448 quote
    Renato Di Lorenzo
    Participant
    Average

    Hi Nicolas.

    The Wiener filter minimizes the mean square error between the estimated random process and the desired process; it is optimum in this sense: there is no other filter that can extract the signal (the trend, or sideways… in our case) out of the noise in a better way, given certain assumptions on the statistical structure of the noise etc.

    The formulas are a little hawkward, and can be found here: https://en.wikipedia.org/wiki/Wiener_filter

     

    Best

    Renato

    06/16/2016 at 3:27 PM #9456 quote
    Nicolas
    Keymaster
    Master

    I can help you, it’s very interesting but I do not understand why this kind of filter has never been re-coded for market data in the past..

    At least, a C++ function or any computerized language of any kind of this math formula would be of great help to recode it for PRT. Thanks.

    06/16/2016 at 4:18 PM #9461 quote
    Renato Di Lorenzo
    Participant
    Average

    I think this is because the formulas are of a higher level of difficulty than is normal for standard technical analysis

    best

    06/17/2016 at 12:46 PM #9497 quote
    mr.brymas
    Participant
    Average

    Hey

    So if I understand then you are looking for a filter that can predict the future by calculating the past and then take positions in the market using the pre-predicted direction of the market? Sounds like advanced coding…

    06/17/2016 at 1:05 PM #9499 quote
    Renato Di Lorenzo
    Participant
    Average

    Hi

    this is what happens normally with technical analysis; in this case the math is quite complicated: https://en.wikipedia.org/wiki/Wiener_filter

    and I’m not sure PRT has the capability to encode it

    best

    renato

    07/08/2016 at 3:51 PM #10319 quote
    Bandido
    Participant
    Average

    I have found the matlab code here:

    http://freesourcecode.net/sites/default/files/57424.zip

    this is the code:

    function Project
%Author: Alex Dytso
%Description: This on of the project that shows how to implement Wiener
%filter as noise cancellations. 
% Our desired response is d(n) ouptut is x(n). We have noise v(n), v1(n)
% and v2(n)
% that have the following relationship v1(n)=0.8*v1(n-1)+v(n) and v2(n)=-0.6v2(n-1)+v(n)
% where v(n) is AWGN. 
% The ouptut is x(n)=d(n)+v1(n)
clc, clear all, close all

%%%%%Part2

theta=2*pi*rand-pi; % generating random varible thetha between -pi and pi
w0=0.05*pi;
N=10000;
n=1:N;

dn=sin(n*w0+theta); %generating our siganl

vn=randn(1,N); %generating 10000 points of White Gaussian Noise


% generating v1n=0.8*v1(n-1)+v(n) and v2(n)=-0.6v2(n-1)+v(n)

v1(1)=vn(1);
v2(1)=vn(1);
for i=2:N
    v1(i)=0.1*v1(i-1)+vn(i);
    v2(i)=-0.05*v2(i-1)+vn(i);
    
end


%generating x(n)=d(n)+v1(n)

xn=dn+v1;


%%%%%Part 3

%ploting xn and dn 
figure(1)
plot(1:200,xn(1:200))
hold on
plot(1:200,dn(1:200),'r')
xlabel('n')
legend('xn','dn')
title('Plot of x(n) and d(n)')
%ploting v2n
figure(2)
plot(1:200,v2(1:200))

xlabel('n')

title('Plot of v_2(n)')
%%%%% part 4 Computing auto-correlation of v2n

%comparing computatation with my function to computation with matlab
rv2=AUTOCORR(v2(1:40)) %computation with my function
rv2m=xcorr(v2(1:40),'biased'); %computation with MatLab

figure(3)
stem(rv2)
hold on
stem(rv2m(20:39),'xr')
xlabel('k')
title('Autocorrlation of v_2(n)')
legend('My function', 'MatLab function')


%%%% part5 Computing cross-correlation between xn and v2n

%comparing computation via my function with computation via MatLab
rxv2=CROSSCORR(xn(1:50),v2(1:50))  %my function 
rxv2m=xcorr(xn(1:50),v2(1:50),'biased');  %MatLab function

figure(4)
stem(rxv2)
hold on
stem(rxv2m(20:39),'xr')
xlabel('k')
title('Cross-correlation between x(n) and v_2(n)')
legend('My function', 'MatLab function')

%%%% part 6  Finding Coefficient of Wiener filter of order 1

%Coefficient are compute by w=Rv2^(-1)*rxv2


Rv2=[rv2(1),rv2(2);rv2(2),rv2(1)] %Autocorrelation matrix of v2


w=(Rv2)^(-1)*rxv2(1:2)  %Coefficients of Wiener fileter of oreder 1


v1nEst=conv(w,v2); %filtering 

dest=xn-v1nEst(1:N); %subtracting estimate of v1 from xn
figure(5)

plot(dest(1:200))
hold on
plot(dn(1:200),'r')
xlabel('n')
title('Estimated d(n) vs actual d(n). Filter order 1')
legend('Estimate d(n)', 'Actual d(n)')
%%%%part 7  order 6
 % autocorrelation matrix 
Rv2ord6=[rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7);
         rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6);
         rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5);
         rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4);
         rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3);
         rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2);
         rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1)]
     
     
     word6=inv(Rv2ord6)*rxv2(1:7)%computing optimal coefficients
     
     v1nEst6=conv(word6,v2);%filtering with Wiener filter
     
     
     
     dest6=xn-v1nEst6(1:10000);%computing the error
figure(6)
plot(dest6(1:200))
hold on
plot(dn(1:200),'r')
xlabel('n')
title('Estimated d(n) vs actual d(n). Filter order 6')
legend('Estimate d(n)', 'Actual d(n)')
%%%part 8

     % autocorrelation matrix 
     Rv2ord12=[rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13);
              rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12);
              rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11);
              rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10);
              rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9);
              rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8);
              rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7);
              rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6);
              rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5);
              rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4);
              rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3);
              rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2);
              rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1)]
          
     word12=inv(Rv2ord12)*rxv2(1:13) %computing optimal coefficients
     
     v1nEst12f=filter(word12,1,v2); %filtering with Wiener filter 
    
     dest12=xn-v1nEst12f(1:10000); %computing the error
     
figure(7)
 plot(dest12(1:200))
 hold on

 plot(dn(1:200),'r')         
 xlabel('n')
title('Estimated d(n) vs actual d(n). Filter order 12')
legend('Estimate d(n) ', 'Actual d(n)')

%%%%part 9 (EXTRA FILTER ORDER 20)


Rv2ord20=    [rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13),rv2(14),rv2(15),rv2(16),rv2(17),rv2(18),rv2(19),rv2(20);
              rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13),rv2(14),rv2(15),rv2(16),rv2(17),rv2(18),rv2(19);
              rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13),rv2(14),rv2(15),rv2(16),rv2(17),rv2(18);
              rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13),rv2(14),rv2(15),rv2(16),rv2(17);
              rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13),rv2(14),rv2(15),rv2(16);
              rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13),rv2(14),rv2(15);
              rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13),rv2(14);
              rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12),rv2(13);
              rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11),rv2(12);
              rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10),rv2(11);
              rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9),rv2(10);
              rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8),rv2(9);
              rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7),rv2(8);
              rv2(14),rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6),rv2(7);
              rv2(15),rv2(14),rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5),rv2(6);
              rv2(16),rv2(15),rv2(14),rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4),rv2(5);
              rv2(17),rv2(16),rv2(15),rv2(14),rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3),rv2(4);
              rv2(18),rv2(17),rv2(16),rv2(15),rv2(14),rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2),rv2(3);
              rv2(19),rv2(18),rv2(17),rv2(16),rv2(15),rv2(14),rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1),rv2(2);
              rv2(20),rv2(19),rv2(18),rv2(17),rv2(16),rv2(15),rv2(14),rv2(13),rv2(12),rv2(11),rv2(10),rv2(9),rv2(8),rv2(7),rv2(6),rv2(5),rv2(4),rv2(3),rv2(2),rv2(1)];


           word19=inv(Rv2ord20)*rxv2(1:20)
     
     v1nEst19=conv(word19,v2);
     dest19=xn-v1nEst19(1:10000);
figure(8)
plot(dest19(1:200))
hold on
 plot(dn(1:200),'r')         
 xlabel('n')
title('Estimated d(n) vs actual d(n). Filter order 19')
legend('Estimate d(n)', 'Actual d(n)')
          
        

%ETRA minimum error

en1=(dn-dest).^2;

en6=(dn-dest6).^2;

en12=(dn-dest12).^2;

en19=(dn-dest19).^2;

J1=mean(en1)
J6=mean(en6)
J12=mean(en12)
J19=mean(en19)

%  figure(9)
%  plot(en1(1:100))
%  hold on
% plot(en6(1:100),'r')
%  plot(en12(1:100),'g')
% plot(en19(1:100),'y')

%%%% EXTRA fft

figure(10)

subplot(4,1,1)
plot(1:200,fft(dest(1:200)))
hold on

subplot(4,1,2)
plot(1:200,fft(dest6(1:200)))

subplot(4,1,3)
plot(1:200,fft(dest12(1:200)))

subplot(4,1,4)
plot(1:200,fft(dest19(1:200)))

end


%%%% Autocorrelation and Cross-correlation functions



function y=AUTOCORR(x) %this function computes autocorrelation
K=length(x);
for index=1:K
    
    y(index,:)=sum([zeros(1,index-1),x].*[x,zeros(1,index-1)])/(K);
end



end


function y=CROSSCORR(X,Z) %this function computes autocorrelation

x=[X,zeros(1,length(Z)-length(X))]; %Making length of x and z to be the same
z=[Z,zeros(1,length(X)-length(Z))];

N=length(z);

for index=1:N
    
    y(index,:)=sum([x,zeros(1,index-1)].*[zeros(1,index-1),z])/(N);
end



end

     

    I think that it is impossible to convert in matlab…

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Wiener Filter


ProBuilder: Indicators & Custom Tools

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Author
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Renato Di Lorenzo @renato_di_lorenzo Participant
Summary

This topic contains 7 replies,
has 4 voices, and was last updated by Bandido
9 years, 7 months ago.

Topic Details
Forum: ProBuilder: Indicators & Custom Tools
Language: English
Started: 06/16/2016
Status: Active
Attachments: No files
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