Talk:Transfer function

message: It would help if common LTI transfer functions (integrator,first order lag, second order lag, lead/lag) were listed here, as they are frequently needed for control system descriptions (e.g. autopilots, etc.). Gordon Vigurs 19:27, 29 May 2006 (UTC)
thread_title: Clearing Up Red Links

message: I was looking for a discussion of Mason's Gain theorem, commonly used in circuit theory and control theory to quickly calculate transfer functions of complicated networks from their signal flow graphs, and was surprised to find that Wikipedia does not have an article on it.  It seems that the Transfer Function page is the most appropriate place to put it.  If no one is already thinking of adding it, I will put in a paragraph on it in the next few days. Mraj 15:22, 13 July 2006 (UTC)
replies: text: go fer it!  i never heard of Mason's Gain Theorem and would be happy for an article on it. r b-j 05:55, 14 July 2006 (UTC)
replies: text: I have never heard of this Mason's gain theorem either, so it would be interesting to see what its about! 8-)--Light current 13:34, 14 July 2006 (UTC)
replies: text:  Check this: Mason's rule Tnae 11:11, 22 August 2006 (UTC)

text: So its actually Masons Rule! AHHH! We dont need a new page then--Light current 15:56, 22 August 2006 (UTC)
replies: text: I added redirects for "Mason's theorem" and "Mason's gain theorem" so there shouldn't be a problem any more. PAR 17:28, 22 August 2006 (UTC)
thread_title: Mason's Gain Theorem

message: The term "transfer function" is also used in Game theory, maybe a disambiguation pointer should be added.  —Preceding unsigned comment added by 169.237.10.220 (talk) 23:26, 11 June 2008 (UTC)
replies: text: If there's an appropriate article to link to, then that may be appropriate.  Oli Filth(talk) 23:33, 11 June 2008 (UTC)
replies: text: This term appears in the article mechanism design. Mct mht (talk) 05:43, 25 April 2013 (UTC)
thread_title:  Meaning in game theory 

message: There is a lot of great info in this article, but for a tyro (and I speak from experience), there's a great big brick wall right at the beginning.  What the heck does "s" represent and what is its form?  I have read half a dozen Wiki articles and others from around the web, and bought two text books.  Still it is not clear.  
It is clear (finally, at long last) is that the domain of a transfer function includes pure imaginary numbers s = j*ω, where ω is a frequency expressed in radians per unit-time (seconds). It is also clear that the range of a transfer function consists of complex numbers whose modulus (aka absolute value, aka L2 norm) represents amplitude or gain, and whose argument (aka angle) represents phase. What is not at all clear to me is whether the domain also includes numbers that are not pure imaginary, and if so what they represent. Everywhere I go I see the formula s = σ + j*ω, without explanation. It seemed to me that σ represents phase-shift in the domain. I expected that when I used a complex number σ + j*ω with a non-zero σ as input to a transfer function, the amplitude output would be unchanged and the phase output would differ from the output for j*ω by σ. Not the case. If I make σ much different from 0, I get nonsense results. Test cases are formulae for audio crossovers and closed box loudspeaker systems whose responses are well-known to me. I know that a loudspeaker's frequency response in SPL does not depend on the phase of the signal.
So my question, which I think this Wiki page should clarify, is what specifically is the domain of a transfer function? Does it include only numbers of the form s = j*ω? If it includes numbers of the form s = σ + j*ω for non-zero σ, what do the those inputs and the associated responses represent?
[I posted essentially the same question on the talk page for "frequency domain."]
Jive Dadson (talk) 08:45, 17 December 2010 (UTC)
replies: text: s is the complex-frequency domain, given by the Laplace transform.  The jω does indeed correspond to pure complex sinusoids, i.e. the Fourier transform.  The σ denotes exponential decay/growth.  Oli Filth(talk|contribs) 12:12, 17 December 2010 (UTC)
thread_title:  Transfer Functions for Dummies 

message: The introductory paragraph is hard for non-specialists to understand. Looking at the article's history someone has tried to improve it by appending a plainly worded sentence.  I suggest the following be considered.  Of course, the rest of the article can continue with technical details but the beginning should be written for those who just want to get to the nut of the idea.  So here goes:
Transfer functions are used (mostly by engineers) to relate an output signal to an input signal.  If  x(t)  represents the time-dependent input signal then the corresponding output signal,  y(t)  will be related (in the most general manner) to the input signal via a function h as,  y(t) = h(x(t),t) .  However the relationship between output and input is usually considered to be linear with respect to  x(t)  so that,  y(t) = h(t)x(t) .  In many fields, such as communications, one usually works in the frequency domain so that x and y are replaced  by their Laplace transforms and we have instead,  Y(s) = H(s)X(s) , where  X(s) = \mathcal{L}(x(t))  and where  \mathcal{L}(.)  is the Laplace transform. (A similar definition applies to  Y(s) .)  The variable s is defined on the complex plane.  If it is restriced to the imaginary axis then the transform is the Fourier transform.
:y(t) = h(t)x(t) is not correct, which points out a glaring omission.  The main body of the article does not mention convolution or the convolution theorem.--Bob K (talk) 14:26, 9 April 2013 (UTC)
thread_title: A Whimsical Definition

message: Hi,
I edited this section to change the symbol which denotes the angular frequency of the arbitrary input from \omega_i to \omega_0.
In more detail, first I expanded this explanation very slightly to actually give a definition of what was then (and now is after my edit was reverted) named \omega_i, so that the line should read:
:A general sinusoidal input to a system of frequency {\displaystyle 2\pi \omega _{0}}  may be written {\displaystyle \exp(j\omega _{0}t)}. 
Then instead of writing the frequency of the general sinusoidal input as 2\pi \omega_i, I substituted 0 for i, so it would read:
:The Laplace transform of a general sinusoid of unit amplitude will be  {\displaystyle {\frac {1}{s-j\omega _{i}}}}. The Laplace transform of the output will be {\displaystyle {\frac {H(s)}{(s-j\omega _{0})}}} and the temporal output will be the inverse Laplace transform of that function:
:{\displaystyle g(t)={\frac {e^{j\,\omega _{0}\,t}-e^{(\sigma _{P}+j\,\omega _{P})t}}{-\sigma _{P}+j(\omega _{0}-\omega _{P})}}} 
Thus the total edit was a few words explaining what \omega actually is, and to change \omega_i to \omega_0 both there and in the subsequent paragraph.
Here is the justification for the change.  The subscript i just earlier actually refers to the i'th pole, and the letter i is the indexing subscript. Here we are starting out with an arbitrary sinusoidal input of amplitude 1 and fixed phase, with frequency f=2\pi\omega, and the function is e^{j \omega t}.
This \omega did need to be decorated by the original author to indicate that it is a particular constant being newly defined in this line. (In other words, a different letter like \tau could be used). The original author decided to do this by applying the subscript i, writing  e^{j\omega_i t}. This occurrence of the subscript i is unfortunate since the same letter is in fact used as a subscript elsewhere in the unrelated context. Namely, i is the indexing subscript for the poles of the transfer function.
It s not absolutely incorrect to re-use the letter i (it was a bound variable in the earlier formula). But it is analagous to writing "Consider \sum_{i=1}^5 i^2.  Let i denote the value of that sum.  An equation like "let i = \sum_{i=1}^5 i^2" is not *wrong*  because i is bound on the right side. But it is not nice grammar.
It is better to write the arbitrary input function by saying if the frequency is 2 \pi \omega_0 the input function is e^{j \omega_0 t}.
In reverting my edit the editor seemed to comment that i should be the indexing subscript for the poles here. There is some vague sense that that could be meaningful in the sense that "now we've chosen to analyze the special case when there is only one pole, let's pretend it is the i'th pole of what we started looking at, and now let's decorate every new variable we introduce with the subscript i."
But that is like saying, when we're considering the i'th pole, that the function of multiplying by 3 is defined by x_i \mapsto 3x_i. 
Again, not wrong, but it would be impossible for someone to understand it without knowing the author's intentions. 
This was immediately reverted with the comment that the i is correctly used as an indexing subscript for the poles in this instance. I feel somewhat surprised that my edit was immediately reverted without anyone contacting me to ask about it.Createangelos (talk) 10:30, 21 February 2018 (UTC)
replies: text: Well, either way it ended up where it should in ....in talk.  This involves some pretty abstract details....variable naming.....which I think is going to limit participation. But, without totally following it,  the above argument sounds good. North8000 (talk) 12:57, 21 February 2018 (UTC)
thread_title:  Gain, transient behavior and stability 

message: The first section of the article makes use of the Laplace transform. I recognize the difficulty in introducing a complicated subject like this, but I wish it could be more accessible to a novice. And by "novice" I include people with advanced degrees in physics who may know Fourier theory but just never happened to learn Laplace theory. At least we do refer the reader to the Laplace Transform article. Is there any way to add enough background here that the reader can at least know what to make of this mysterious variable s?  I think it would help to include some mention of the exp(st) while stopping short of the full theory.  For example, 
"The variable s is a complex number with the units of angular frequency. Assuming a signal has the time dependence V(s)exp(st), the filter described by H(s) will transform the signal to H(s)V(s)exp(st)."  
Any better ideas?  Leave it be?  Spiel496 (talk) 16:22, 23 June 2020 (UTC)
thread_title:  Suggest some background on the Laplace domain 

message: is is too much to ask for engineers to get even the most basic mathematical terminology right?2A01:CB0C:CD:D800:A09D:2552:BEC9:53AA (talk) 14:18, 21 September 2020 (UTC)
thread_title:  " In its simplest form, this function is a two-dimensional graph"