A question on Laplace transform

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Discussion Overview

The discussion revolves around the relationship between two functions, x(t) and y(t), defined by the equation y(t) = 1/(x(t) - k). Participants explore how to derive the ratio Y(s)/X(s) using Laplace transforms, considering different interpretations of the relationship and the implications for signal processing.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests deriving Y(s)/X(s) by expanding the inverse term in a Taylor series, noting that this could lead to convolution in the Laplace domain, which they find complicated.
  • Another participant interprets the relationship as y(t) = 1 / x(t - k), arguing that this formulation makes more sense for causal systems, as it implies y(t) depends on the past values of x(t).
  • A different participant questions the original formulation of y(t) and expresses confusion about the lack of specification regarding the variable x in the denominator.

Areas of Agreement / Disagreement

Participants express differing interpretations of the relationship between x(t) and y(t), with no consensus reached on the correct formulation or approach to derive Y(s)/X(s).

Contextual Notes

There are unresolved assumptions regarding the definitions of x(t) and y(t), as well as the implications of the time shift represented by k. The discussion does not clarify the nature of k or its role in the relationship.

Who May Find This Useful

This discussion may be of interest to those studying signal processing, control systems, or Laplace transforms, particularly in the context of causal relationships between input and output signals.

Debdut
Messages
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x(t) and y(t) are related by y(t)=1/(x(t) -k), how should I derive Y(s)/X(s)?
 
I'm thinking of expanding the inverse term in its Taylor series form. But it would involve terms like (x(t))^2, (x(t))^3, etc if I am right. That would lead to convolution in Laplace domain which according to me is becoming more complicated!
 
I cannot make sense of the question. Here is what I think, y is the "output" and x is the "input" and the relationship is supposed to be y(t) = 1 / x( t - k )
Note I have put the " - k " inside the function argument. This way it has y(t) depending on what x(t) was k seconds ago. This makes more sense since input/output signals in the time domain should be causal and not responding instantaneously. Although maybe I'm missing the point of the question entirely.
 
Then again, why do they put x downstairs without even specifying what it is?
 

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