On Oct 10, 8:01&#4294967295;pm, "Zeph80" <surabhi_tal...@hotmail.com> 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?


Here is an actionscript program that may help you see what you are
trying to figure out:

http://www.fourier-series.com/fourierseries2/flash_programs/LowPassFIR/index.html



http://www.fourier-series.com/fourierseries2/convolution.html

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 temporal 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 

On 11 Okt, 02:01, "Zeph80" <surabhi_tal...@hotmail.com> 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.

No. One doesn't select the sampling frequency quite as
freely as that. The sampling frequency is the dominating
system parameter, it's the hardest parameter to change.
So one chooses it with a lot of safety margin just to
be sure one doesn't loose soemthing that might be
important.

So once you get to filtering one particular signal you
have to accept whatever sampling frequency was used, and
go on from there.

> Why is this?Isn't the frequency resolution that I specify for the filter
> response going to be poorer as I choose higher Fs?

No. The 'frequency resolution' is compensated by using
more coeffcients in the filter. If you do the math
you will find that it is the temporal duration of the
filter that is important, not the number of coefficients.

In other words, if a filter with sampling frequency f'
requires 9 samples to meet a (physical frequency) spec,
a filter with sampling frequency f" = 10*f' will require
10*9 = 90 samples to meet the same (physical frequency) spec.

The two filters have different numbers of coeffcinets but
their impulse responses last for the same (physical) time.

Rune

What you said may be true, but it is not a very fruitful way of looking at
the problem.  Three reasons I can think of: First, the sampling rate is
usually determined by other factors, such as the nature of the signal, the
analog processing done before the ADC, and the computational power of your
processor. It is not something that you adjust to faciliate the algorithm.


Second, it is easy to made N larger if you want better resolution in your
frequency response specification. 

Third, and most important, the frequency resolution of your final filter
does not usually depend on the accuracy of your initial specification. It
depends mainly on the length of the filter kernel.

Here's two links that may help. 
Regards,
Steve

http://www.dspguide.com/ch16/1.htm
http://www.dspguide.com/ch17/1.htm

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?

You choose the sample rate to meet or exceed the signal's requirements. 
You choose N to provide the number of taps that you think your filter 
will need. More taps give better control of response at the cost of more 
delay and greater processing burden.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
** Posted from http://www.teranews.com **

>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?

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?

First of all, what are you calling N? I can think of a few alternatives.

Basically, Fs is determined by other system constraints, not the least 
of them being the highest frequency present in the signal.

Avoid the issue. For equiripple design, use something like 
http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFiltDes102.html. Your 
choice of windows is a bit limited, but probably adequate.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
** Posted from http://www.teranews.com **

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?