Formula Manipulation/substituion and Simplification

Hello everybody,

I have a analog transfer function like below

H(S) = (b10 * S^10 + b9 * S^9 + b8 * S^8 + b7 * S^7 + b6 * S^6 + b5 * S^5 + b4 * S^4 + b3 * S^3 + b2 * S^2 + b1 * S^1 + b0) / (a10 * S^10 + a9 * S^9 + a8 * S^8 + a7 * S^7 + a6 * S^6 + a5 * S^5 + a4 * S^4 + a3 * S^3 + a2 * S^2 + a1 * S^1 + a0) where some times b11/a11 to b20/a20 variables will add to above expression.

Now i want to substitute S = 2/T*(1-Z^-1)/(1+Z^-1) and finally i wants to get the formula some this like below

H(Z) = (some_expression_consists_of_b(n)_a(n) + some_expression_consists_of_b(n)_a(n) * Z^-1 + some_expression_consists_of_b(n)_a(n) * Z-2 + .... + some_expression_consists_of_b(n)_a(n) * Z^10) / (1 + some_expression_consists_of_b(n)_a(n) * Z^-1 + some_expression_consists_of_b(n)_a(n) * Z-2 + .... + some_expression_consists_of_b(n)_a(n) * Z^10)

I tried many functions present in symbolic toolbox and finally lost. Can you please let me know how to solve the above problem using symbolic toolbox

Answer 1

[Fei Deng]

Did you try function "subs"? https://www.mathworks.com/help/symbolic/subs.html

For example if originally you have H(s) = a1+b1*s, you then want to substitute s with 2*t*z:

>> syms a1 b1 s t z

>> subs(a1+b1*s, s, 2*t*z )

ans = a1 + 2*b1*t*z