talking
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my questions is about the relationship between polynomial modeling and transfer function.
As well known, the transfer function h(t) for LTI system has the relationship between input x(t) and output y(t):
y(t) = x(t) * h(t) ----- eq(1)
where * is convolution operation.
Then, a system is modeled using a polynomial series as
y(t) = Σ a(i) [x(t)]^i ----- eq(2)
where i is an index for the polynomial series, and a(i) is the polynomial coefficient.
Here is a question.
The polynomial model itself " Σ a(i) [x(t)]^i " in eq(2) corresponds to
" x(t) * h(t) " in eq(1)
OR
" h(t) " in eq(1)?
I'm asking because a polynomial model which represents a certain system is considered as "transfer function" of the system in some articles.
As well known, the transfer function h(t) for LTI system has the relationship between input x(t) and output y(t):
y(t) = x(t) * h(t) ----- eq(1)
where * is convolution operation.
Then, a system is modeled using a polynomial series as
y(t) = Σ a(i) [x(t)]^i ----- eq(2)
where i is an index for the polynomial series, and a(i) is the polynomial coefficient.
Here is a question.
The polynomial model itself " Σ a(i) [x(t)]^i " in eq(2) corresponds to
" x(t) * h(t) " in eq(1)
OR
" h(t) " in eq(1)?
I'm asking because a polynomial model which represents a certain system is considered as "transfer function" of the system in some articles.