[help] how to prove this equation

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Discussion Overview

The discussion revolves around proving a specific equation presented in a linked image. Participants are exploring the components of the equation and discussing methods for establishing its validity, with a focus on mathematical reasoning and inequalities related to integrals.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant requests clarification on the variables s, σ, j, and ω, questioning whether they are constants and their potential values.
  • Another participant identifies s as a complex number.
  • A participant suggests using an inequality for integrals, stating that the absolute value of an integral is less than or equal to the integral of the absolute value.
  • There is a discussion about the expression |e^{-s}|, which is broken down into |e^{-σ}| and |e^{-jω}|, prompting further inquiry into the value of |e^{-jω}|.
  • Another participant reiterates the inequality involving integrals, emphasizing its relevance to the discussion.

Areas of Agreement / Disagreement

Participants are engaged in a collaborative exploration of the problem, with some clarifications and suggestions made, but no consensus or resolution has been reached regarding the proof of the equation.

Contextual Notes

There are missing definitions and assumptions regarding the variables involved, and the discussion does not resolve the mathematical steps necessary for the proof.

goodness52200
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http://xs305.xs.to/xs305/06332/ss.gif

Hello all, how to prove the above equation
thanks a lot
 
Last edited by a moderator:
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Could you explain what [tex]s, \sigma , \ j, \ \omega[/tex] are? Are they constants, negative or positive?
 
hi ViettDao29
s is a complex
 
Oh... so j is our usual i=sqrt(-1) :-p
Use an inequality for integral that absolute value of integral is less than or equal to integral of absolute value. Then consider that

[tex] |e^{-s}| = |e^{- \sigma}| |e^{-j \omega}|<br /> [/tex]

Now, what is [itex]|e^{-j \omega}|[/itex] ?
 
Last edited:
Also recall that [tex]\, \left| \int f(x) \, dx\right| \leq \int\left| f(x) \right| \, dx[/tex]
 

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