FIR Filters using frequency Sampling

Hello All

      Our application is channel embed/de-embedding. The frequency
characteristics of the channel are specified in a  (S-parameters
file).

   To generate an FIR filter, matching the specified frequency
response, Frequecny sampling method using IFFT is used.

   We have been able to use this with limited success.

   I am looking for the limitation's of this IFFT method -
   Can this method be used to match arbitrary magnitude and phase
respones? or there are any constraints to it?
   Can the phase input be non-linear?


   Also,Which are the other popular methods, that can be ued for this
purpose?


Thanks in advance
Partha

parth175@yahoo.co.in wrote:
> Hello All
>
>      Our application is channel embed/de-embedding. The frequency
> characteristics of the channel are specified in a  (S-parameters
> file).
>
>   To generate an FIR filter, matching the specified frequency
> response, Frequecny sampling method using IFFT is used.
>
>   We have been able to use this with limited success.
>
>   I am looking for the limitation's of this IFFT method -
>   Can this method be used to match arbitrary magnitude and phase
> respones? or there are any constraints to it?
>   Can the phase input be non-linear?
>
>
>   Also,Which are the other popular methods, that can be ued for this
> purpose?

Partha,

This is a fairly gross way of doing things.  It's the simplest form of the 
"windowing" method.  It's subject to strong Gibbs phenomenon at sharp 
transitions in frequency.  It's as if you convolve the wanted frequency 
response with a sinc-like Dirichlet function.  The sidelobes of this 
function are pretty big.  That's a big limitation.

The windowing method goes like this:
Knowing that the large sidelobes of the sinc or Dirichlet are a bit of a 
problem, we opt for a better function.  In general, this function will have 
a wider main lobe and lower sidelobes.  From there you can think about all 
sorts of goodness criteria.

The IFFT of this function will generally be large in the middle and tapered 
at the edges.

So, you select this function and convolve the desired frequency response 
with it before doing the IFFT.

Or, equivalently, you can select the function (the "window") in the time 
domain and multiply the IFFT of the ideal frequency response with it.

Then, as a check of the latter method, FFT the result to see the frequency 
response thus obtained.

"Can this method.....?" I don't see why it can't do just about anything you 
want - within the limits of physics.  The limits of physics may surprise you 
or frustrate your objectives.

"Other popular methods for *what* purpose?  Designing FIR filters in general 
or a specific type or with a specific objective??  The Parks-McClellan 
program is very popular for designing FIR filters with symmetric / 
antisymmetric temporal structure.  i.e. linear phase.

Fred

On Dec 19, 12:22 am, parth...@yahoo.co.in wrote:
> Hello All
>
>       Our application is channel embed/de-embedding. The frequency
> characteristics of the channel are specified in a  (S-parameters
> file).
>
>    To generate an FIR filter, matching the specified frequency
> response, Frequecny sampling method using IFFT is used.
>
>    We have been able to use this with limited success.
>
>    I am looking for the limitation's of this IFFT method -
>    Can this method be used to match arbitrary magnitude and phase
> respones? or there are any constraints to it?
>    Can the phase input be non-linear?
>
>    Also,Which are the other popular methods, that can be ued for this
> purpose?
>
> Thanks in advance
> Partha

Take a look at:

http://ccrma.stanford.edu/~jos/sasp/FIR_Digital_Filter_Design.html

It explains the frequency sampling approach and it's limitations as
well as the window approach and others.

Dale B. Dalrymple