How to implement triple summation?

[darova]

DO you have any attempts?

[Jan]

What are h_p? What is the meaning of h_p^(q, p-q)? What is X*? Do you want a symbolical or numerical summation?

[Usha Sree Katikala]

I have made an attempt in implementing individual parts of this equation.I need help in combining them as triple summationThe code is:

.

clear all
close all
[x1,Fs] = audioread('C:\Users\admin\Downloads\OSR_us_000_0061_8k.wav');  % audio signal assumed as transmitted signal
 values= x1(1:100);    % array of received signal x(n)
Nsamps = 100;       % number of samples taken from the input signal
 
t = (1/Fs)*(1:Nsamps)    
  plot(t, values)
title('signal');
 xlabel('Time');
 ylabel('Amplitude of signal');
xc=complex(values); % complex of received signal 
%SI Signal model
p=3;  % high non-linearity order
q=2;
M=0;    % memory length
for i= 0:q
    M=M+1;
    first=2*(delayseq(values,M));    %  x(n-m)^q
end
M=0;
for i=0:p-q
    M=M+1;
    xc1= 2*(delayseq(xc,M));          % x*(n-m)^p-q    
end
 
cf=first.xc1;    % x(n-m)^q * x(n-m)^p-q
 
g=1.012;  %g-> gain imbalance 
phi=1;   % phi-> phase imbalance.
 
%%% K1 and K2 are the constants in the IQ Modulator output signal%%%
%%% model(frequency independent model)%%%
 
K1=1/2*(1+g*exp(i*phi));     %   K1
K2=1/2*(1-g*exp(i*phi));     %   K2
K1abs=abs(K1);               %   |K1|
K2abs=abs(K2);               %   |K2|
%%% h1,h2,h3,h4 are Basis function coefficients  for P=3 %%%
 
h1=K1*K1*complex(K2);
 
h2=(power(K1abs,2)K1)+(2(power(K2abs,2)*K1));
 
h3=2*(power(K1abs,2))*K2+power(K2abs,2)*K2;
 
h4=K2*K2*complex(K1);

Can someone help me to solve the triple summation part?

Answer 1

[Matt J]

Well, for each fixed p and q, the inner sum over m is just a discrete convolution. So, perhaps the best solution is to do a double loop over p and q and add up conv() output.

r=0;
for p=1:P
 for q=0:p

       r=r+conv(____,shape)
    
  end
end

One advantage to this approach is that you can use conv's 3rd argument shape to deal with array edge conditions.