Re: transfer function


"deneme" <ozgurklc@xxxxxxxxx> wrote in message
news:1152352856.211449.91810@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hi,

The fir central frequans :40 khz batwith :10 khz . How can i find the
transfer function? T(s)?


T(s) would suggest continuous time and FIR implies (but does not necessarily
mean) discrete time. T(z) would suggest discrete time.
So, this should be clear.

First you're going to need a better definition of the frequency response of
the filter or anything you come up with will be an approximation.


Since you said T(s), here might be an approach:

Design a FIR filter with the desired frequency response.
Notice that a FIR filter is nothing more than the sum (superposition) of a
bunch of weighted delays.
So, we can use superposition and look at each weighted delay as one
component.
Each delay transforms like this:

L{f(t-d)} = e^-ds*F(s) where d is the delay and F(s) is the Laplace
transform of f(t) with no delay.

Each "tap" on a FIR filter would have a transform:

L{f(0)} = An

for each coefficient value A(sub n) (treating each tap response as an
impulse response)

So, by superposition, a FIR filter would appear to have a Laplace Transform
that can be expressed as:

{a0*e^-D0s + a1*e^-D1s + a2*........} Where D0, D1, etc. are the delays for
each tap and a0, a1, a2, .... are the weights or coefficients.

Then because there may be some symmetry around the center of the filter,
some of these terms may combine in interesting ways. I'll leave the math up
to you.

Fred





.

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