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Q&A Meaning of complex frequency [closed]

0 answers  ·  posted 3mo ago by MissMulan‭  ·  closed 3mo ago by MissMulan‭

#3: Question closed by user avatar MissMulan‭ · 2022-07-10T18:43:25Z (3 months ago)
#2: Post edited by user avatar Canina‭ · 2022-07-10T18:43:08Z (3 months ago)
typeset formulae as formulae, not images
Meaning of complex frequency
  • If we have a LC high pass filter the transfer function H(s) becomes:
  • ![](https://physics.codidact.com/uploads/9ebwwQ7uz2nhUmVCM8WQow4u)
  • If we solve for s to find a pole of the transfer function we get:
  • ![](https://physics.codidact.com/uploads/YFvV7yjmhDkMFSb1XatGiyxD)
  • In the case of a sinusoidal input signal = s = jω -> ω = 1/sqrt(LC)
  • But in a case of a signal which may not be sinusoidal s can be a complex number and the result of this is that the pole exists at a complex frequency.But what physical meaning does a complex frequency have?
  • If we have a LC high pass filter the transfer function H(s) becomes:
  • $$ H(s) = \cfrac{sL}{sL + \cfrac{1}{sC}} $$
  • If we solve for s to find a pole of the transfer function we get:
  • $$ s = j \cfrac{1}{\sqrt{LC}} $$
  • In the case of a sinusoidal input signal = $ s = j \omega \rightarrow \omega = \cfrac{1}{\sqrt{LC}} $
  • But in a case of a signal which may not be sinusoidal s can be a complex number and the result of this is that the pole exists at a complex frequency. But what physical meaning does a complex frequency have?
#1: Initial revision by user avatar MissMulan‭ · 2022-07-08T18:15:32Z (3 months ago)
Meaning of complex frequency
If we have a LC high pass filter the transfer function H(s) becomes:

![](https://physics.codidact.com/uploads/9ebwwQ7uz2nhUmVCM8WQow4u)

If we solve for s to find a pole of the transfer function we get:

![](https://physics.codidact.com/uploads/YFvV7yjmhDkMFSb1XatGiyxD)

In the case of a sinusoidal input signal = s   = jω -> ω  = 1/sqrt(LC)

But in a case of a signal which may not be sinusoidal s can be a complex number and the result of this is that the pole exists at a complex frequency.But what physical meaning does a complex frequency have?