FIR filter sampling frequency

"Jerry Avins" <jya@ieee.org> wrote in message 
news:wcidnUdqsb87AcrZnZ2dnUVZ_t-dnZ2d@rcn.net...
> Zeph80 wrote:
>> I have some questions regarding the sampling frequency of a digital 
>> filter?
>> This is the rate at which the internal stages are clocked, why does this
>> have to be twice the incoming data rate. I don't understand where Nyquist
>> comes in the filter design.Our incmoing data was generated by sampling a
>> analog at twice frequency, and now my filter must run at twice the data
>> rate.Why?
>
> There seems to be a bit of confusion. The sample rate has to exceed twice 
> the highest frequency that the analog signal might contain. Once sampling 
> is accomplished. the sample rate _is_the data rate.
>
> Jerry

Jerry is correct and that should settle it.

Normally a FIR filter "unit delay" or the time associated from one 
coefficient to the next is the same as the time between data samples - the 
reciprocal of the sample rate.

In some specialized situations the unit delay of a FIR filter might be a 
multiple of the sample interval.  If this is done, the filter's frequency 
response *repeats* between zero and fs.  A comb filter is an example of 
this. The simplest case of this would have every other coefficient set to 
zero and the frequency response would repeat once.  A half-band filter 
almost looks like this - with the exception of the middle coefficient and 
its delay - every other coefficient is zero and the filter response repeats.

I don't know of a method where the filter sample rate is higher than the 
data rate but it's certainly possible.  This could result in a filter that 
looks like it's periodically time-varying.  One set of coefficients for 
time=0, another for time=1, another for time=2 and then back to those for 
time=0 for a span of 3 sample intervals.  Of course, doing this triples the 
output sample rate.  It's as though you took the data and added 2 zeros in 
between each sample to increase the sample rate and then passed the result 
through the same filter.  Now the filter no longer looks time varying and 
the signal is repeated 3 times between zero and the new fs.

Fred