how to write the transfer function of the expression

how to write the transfer function of the expression in Z domain.

Answer 1

[Walter Roberson]

num = 5;
denom = zeros(1, 71);
denom(20+50+1) = 10;
denom(-20+50+1) = 2;
denom = fliplr(denom);
g = tf(num, denom);

Except that theoretically what you posted has an additional 50 poles at 0.

[phoenix]

how to convert this to z domain:g(Z)

[Walter Roberson]

z = tf('z);
T = 5*z^(-50)/(10*z^20+2*z^(-20))

[phoenix]

Thanks for the help.But if i put A(:,1)matrix element and B(:,1) in place of 10 and 2 respectively,it does not works.

[Walter Roberson]

Are those A and B values numeric?

[phoenix]

Yes,a set of n elements(suppose).but A and B are different.

[Walter Roberson]

Are you trying to create a MIMO system?

The below takes a while to execute, and I doubt it is what you want as it would be 5 inputs and 5 outputs. I suspect you want 1 input and 5 outputs

N = 5;

num = 5;

A = randi([-10 10], N, 1);
B = randi([-10 10], N, 1);

z = tf('z');
T = repmat(num * z^(-50), [N, N]) / repmat(A(:,1) * z^20 + B(:,1) * z^(-20), [1, N])

Let's see:

N = 5;

num = 5;
num = repmat({num}, [N, 1]);

A = randi([-10 10], N, 1);
B = randi([-10 10], N, 1);
denom = zeros(N, 71);
denom(:,20+50+1) = A(:,1);
denom(:,-20+50+1) = B(:,1);
denom = fliplr(denom);
denom = num2cell(denom, 2);

g = tf(num, denom, -1);

Ah, that looks more plausible.

[phoenix]

It is showing this error- Undefined function or method 'randi' for input arguments of type 'double'

[Walter Roberson]

randi was added in R2008b. If your MATLAB release is older than that, then we need to know which release you are using in order to give us a chance to test things out for your old software.

[phoenix]

R2007b

[Walter Roberson]

N = 5;

num = 5;

A = rand(N, 1) * 20 - 10;    %create SOME data for A, since user did not tell us what the values should be
B = rand(N, 1) * 20 - 10;    %create SOME data for B, since user did not tell us what the values should be

z = tf('z');
T = repmat(num * z^(-50), [N, N]) / repmat(A(:,1) * z^20 + B(:,1) * z^(-20), [1, N])

[phoenix]

Thanks Walter for your prompt reply in solving the problem.I have attached the details.

[phoenix]

Anyone there to help???

[Walter Roberson]

N = 5;

num = 5;

A = rand(N, 1) * 20 - 10;    %create SOME data for A, since user did not tell us what the values should be
B = rand(N, 1) * 20 - 10;    %create SOME data for B, since user did not tell us what the values should be

z = tf('z');
T = repmat(num * z^(-50), [N, N]) / repmat(A(:,1).^2 * z^20 + B(:,1).^2 * z^(-20), [1, N])

[phoenix]

I have attached the problem in details.I have specified A and B. but you didnt reply accordingly @ Walter Roberson.

[Walter Roberson]

rand(N, 1) * 20 - 10 and rand(N, 1) * 20 - 10 are polynomial coefficients... for some polynomial or other.

We need numeric values for A and B for testing purposes, to prove that the function works. It is not possible for us to program in, for example,

 A = syms('A', [5, 1]);
 B = syms('B', [5, 1]);

to use A1, A2, A3, A4, A5, B1, B2, B3, B4, B5 as symbolic coefficients. Transfer functions created with tf() cannot use symbolic coefficients: they can only use purely numeric coefficients.