Formula Manipulation/substituion and Simplification

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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

Answers (1)

Fei Deng
Fei Deng on 17 Apr 2017
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

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