Zeph80 wrote:
>> In windowing method for FIR design, you specify the frequency
>> response of the desired filter at sample points fs/N, and perform an
>> IDFT to obtain h(n).
>> So doesnt this mean that you want fs to be as low as possible to
>> specify better frequency resolution. But Fs is generally many times
>> the cut-off frequency - more than the minimum of twice the cut off
>> needed.
>>
>> Why is this?Isn't the frequency resolution that I specify for the
>> filter response going to be poorer as I choose higher Fs?
>>
>>
>
>
> N is the size of FFT. I guess my question is, when I design this
> filter using the IDFT method, if I had a choice how would I select Fs
> and why?
I think I see how you got there ....
- if you assume that the length of the filter is fixed already then
- then, you note that the sequence to be IDFTd is spread over Fs
- then, the samples in the sequence move apart as Fs is increased.
You ask if the sample rate should not be as low as possible and the answer
is YES. No design should have it higher than "necessary" - and
"necessary"
is in the eye of the beholder for a number of reasons.
I think you probably understand by now:
- the length of the filter will be determined by the sharpness of
transitions between stop bands and pass bands .. because it forces the
distance between frequency sample points. The closer the frequency sample
points have to be, the longer the filter has to be.
- the tem****al sample interval is the unit delay in the filter
So:
- given that the sample rate is determined by other factors anyway (as
others have pointed out), it will be a low as possible before you reach
the
point of filter design. Well, except in more complicated cases.
- you sample the intended frequency response as densely or as sparsely as
your specification can stand. This determines the length of the filter.
As long as you assume that the sample rate is as low as possible, then the
filter length is pretty much fixed by your frequency response
specification.
I hope this helps.
Fred
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