[sdiy] Transfer Functions

[Wooster Audio]

I've been reading "Introduction to Digital Filters" by Julius O Smith - 
great online FREE book, so this is all fresh in my head.

   http://www.dsprelated.com/dspbooks/filters/

The transfer function for an analog signal is called H(s), where

    H(s) = Y(s) / X(s).

Y(s) is basically the frequencies at the output, and X(s) is the 
frequencies at the input.  So when you take the input signal X(s) and 
mulitply it by the transfer function H(s) you get the output signal Y(s)

   Y(s) = X(s) H(s)

Thus the transfer function represents what the filter does to the 
frequencies in a signal.  Starting from a time domain description of the 
inputs and outputs, y(t) and x(t), you can find out what the frequency 
domain Y(s) and X(s) are by using something called the Laplace 
transform.  The digital equivalent of H(s) is H(z), which you figure out 
using the z-transform.

Nathan

On 7/15/2010 4:16 PM, Stewart Pye wrote:
> With the talk of transfer functions of filter circuits I'm wondering 
> if someone could point me to somewhere on the internet or a book that 
> would help me to learn this...
>
> I studied electronics (advanced diploma) at a technical college about 
> 12 years ago and do recall touching on this, but I'd have to re-learn 
> the mathematics as I wasn't really interested in it at the time, 
> however I did pass subjects that delt with imaginary numbers and such 
> things. I just can't remember!. Until now I've usually been able to 
> get by with things like f = 1/2*pi*R*C.
>
> Cheers,
> Stewart.
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