# square root of s domain transfer function

I have a question about calculating the square root of the magnitude of a transfer function. When you take the square root, what is happening? My initial idea of a magnitude is a single value, but in this case, the magnitude changes with respect to frequency. So in effect, are you left with an array of values? As well, what is happening to the phase?

The reason I am asking this is because I am having trouble to evaluate the following equation

$$\sqrt(||sys||^2+||sys2||^2)$$

where sys and sys2 are transfer functions.

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It would be very unusual to take the root of the magnitude??? And certainly the magnitude varies with frequency. Think of a simple low-pass filter. The magnitude is about $1$ during the pass band and then drops off rapidly. Perhaps I am missing something in your question? – copper.hat Jun 25 '12 at 5:35
@copper.hat to answer your first question, i am computing the magnitude of a complex number so ||A||^2 = AA*, where A = A_1+A_2 e^{st}+A_3^{-st} So when you do the multiplication you have the terms ||A_1||^2, ||A_2||^2 and ||A_3||^2 pop up (along with some exponential terms). So, to get ||A||, you have to square root each of the above terms somehow, which is where I am stuck. Hope that clears up my question. Thanks. – suzu Jun 26 '12 at 3:57