- #1
hilman
- 17
- 0
Can anybody explain to me briefly on why in a transfer function like G(s), we substitute s=jw such that it become G(jw) in order to find its gain value?
Thanks
Thanks
a big thing in looking at systems like this is knowing if they are linear and if they are time invarient.hilman said:Wow, I like your answer. I am still a beginner in this kind of things and I can understand most of your answer. But one question. What is exactly a linear system?
Thanks in advance
donpacino said:a big thing in looking at systems like this is knowing if they are linear and if they are time invarient.
you should know these
Linear:: more or less to be a linear system the sum of two inputs have to equal the sum of the two outputs
x1(n)=y1(n)
x2(n)=y2(n)
so in order to be linear
x1(n)+x2(n)=y1(n)+Y2(n)
then continue that out to inf and -inf
basically, this means if you graph the system, it will be a straight line.
for a system that is time invariant, delaying the input by a constant delays the output by the same amount.
given the system x(t)=y(t)
x(t-d)=y(t-d) for all values of t and d
The variable "s" represents the complex frequency domain in a transfer function, while "jw" represents the imaginary component of the frequency domain. This replacement allows for easier mathematical manipulation and analysis of the transfer function.
Replacing "s" with "jw" does not change the transfer function itself, but rather represents a different representation of the same function. It allows for the transfer function to be analyzed in the frequency domain instead of the time domain.
Yes, other variables such as "ω" or "f" can be used instead of "jw" in a transfer function. However, "jw" is the most commonly used variable as it clearly represents the imaginary component of the frequency domain.
The variable "s" is commonly used in the original transfer function because it represents the Laplace transform variable, which is commonly used in control systems and signal processing. The use of "s" also allows for the transfer function to be analyzed in the Laplace domain.
The replacement of "s" with "jw" does not change the location of the poles and zeros in the transfer function. They are still located at the same points in the complex plane. However, the substitution allows for easier identification and analysis of the poles and zeros in the frequency domain.