Laplace transform and fourier transform

ninju said:

@pancho_hideboo: you're turning this into an argument. I disagree that we "don't use s in physics" but thats a different topic. I meant you to read and understand what complex numbers mean in real world. Mathematics is, but a tool to understand physics, so no point if you know 2+2=4 unless you know what it actually means.

What exactly did you mean to say by giving the wikipedia link?

---------- Post added at 22:34 ---------- Previous post was at 22:32 ----------

yeah sorry about leaving t out, felt lazy to type it. Didn't expect people to point out things which are meant to be implicitly understood. Please accept my apologies for that.

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ninju said:

From our conversation, i gather that you are incorrigible.

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pancho_hideboo said:

Consider eigen mode of 1/(1-jw), that is, Inverse Fourier Transformation.

It is "exp(t)".

The Designer's Guide Community Forum - Bode Diagram of Conditionally Stable System

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pancho_hideboo said:

Wrong.

Any of 1/(1+s), 1/(1-s), 1/(1+j*w) and 1/(1-j*w) can exist actually.
Fourier Transformation and Laplace Transformation are same from point of view of complex function theory.
Consider "Analytic Continuation". Here w is complex number.
Difference is a trivial, we use complex variable "s" or "w".

Surely read my append.

(1) In studying stability of system, an important factor which we have to focus on is "Characteristics Polynomial" not "Input to Output Transfer Function"

(2) Fourier Transformation and Laplace Transformation are mathematically same.
Consider "Analytic Continuation" in complex function theory.
Especially they are completely same for causal function.

(3) Even if you charcaterize circuit by H(jw) instead of H(s), "eigen mode" is same.
So there is no difference between H(jw) and H(s) regarding "eigen mode".

(4) Even if gain is lesser than 0dB, circuit could be unstable.
Here you have to understand "eigen mode".

(5) In small signal AC analysis, "eigen mode" is never generated.
Consider time domain equation in stead of AC analysis.

(6) Consider simple RC-lowpass filter.
H(jw)=1/(1+j*w/wc), where wc=R*C.
If R is negative, wc is negative.
Consider time domain phenomena,.
If "eigen mode", exp(-t*wc) excited by some noise will grow infinitely since wc<0. This is due to negative resistance.

Again surely read my append.
Again Fourier Transformation and Laplace Transformation are mathematically same.

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