FFT: Could you help me to clarify some doubts?

Hi
could someone read my last post and check if i have understand good?
Thanks

On 10/28/2011 5:53 AM, gpezzella wrote:
> @Wescott
> Hi Tim, I have read your sampling.pdf article. It is the most clear article
> on
>
> Antialiasing ever read. If you have other article please send me a link.
>
> If I have understand good, I must remove frequency over Fsampling/2
> *before* acquire the signal and I must do it with analog filter.

Of course. The aliases mix with the wanted signal and there's no way to 
separate them.

> Since is pratically impossible have super high order low pass filter, is
> better first improve the sampling rate frequency and if not was sufficient
> reduce a cutoff frequency of the analog filter.

Oversample to the point where anti-aliasing becomes easier to 
accomplish. A numerical example:

Maximum desired signal frequency ......................... 10 KHZ
Minimum sampling frequency* .............................. 20 KHz
Lowest frequency in the signal that can alias ........ 20.001 KHz
Minimum allowable alias attenuation ...................... 40 dB
Anti-alias filter requirement ............................. Ouch!

OK. Let's try again:
______________________________
* Ignoring resolution time

Maximum desired signal frequency ......................... 10 KHZ
Sensible sampling frequency .............................. 30 KHz
Lowest frequency in the signal that can alias ........ 20.001 KHz
Minimum allowable alias attenuation ....................... 40 dB
Anti-alias filter requirement ....................... Not so bad.

Signals above 15 KHz will alias into the samples you get, but you can 
filter out anything above 10 KHz digitally, after sampling. Just above 
15 KHz will have an alias at just below 15 KHz. 20 KHz will appear as an 
alias at 10 KHz, and your filter will have to attenuate the 20 KHz 
signal 40 dB relative to a signal at 10 KHz. That's doable, but not 
easy. Work out what you need if the sample rate is increased to 40 KHz. 
You will see that the analog filter will be much easier to build. How 
high must the sample rate be to allow a simple R-C to do the job?

   ...

Jerry
-- 
Engineering is the art of making what you want from things you can get.

On Fri, 28 Oct 2011 04:53:18 -0500, gpezzella wrote:

> @Wescott
> Hi Tim, I have read your sampling.pdf article. It is the most clear
> article on
> 
> Antialiasing ever read. If you have other article please send me a link.

Thank you.

Try these: http://www.wescottdesign.com/articles.html

> If I have understand good, I must remove frequency over Fsampling/2
> *before*
> 
> acquire the signal and I must do it with analog filter.
> 
> Since is pratically impossible have super high order low pass filter, is
> better first
> 
> improve the sampling rate frequency and if not was sufficient reduce a
> cutoff
> 
> frequency of the analog filter.
> 
> In this mannery I avoid to introduce unexpected aliased energy into my
> interested
> 
> range of frequency.

Correct.  Don't lose sight of the fact that you can sample fast with a 
really cheap analog filter, filter again in digital-land where it's easy 
to get precision filters, then decimate (re-sample) the resulting signal 
down to your final rate.

> Now I need suggest that come from real experience into real world. This
> is my case:
> 
> ******************************************************************* I
> have a Microwave Sensor that detect human being presence (google
> innosent ipm 65
> 
> and click on first result that will appeare). When human being is
> detect, IPM 65 return in output frequency from 6Hz - 600Hz.
> *******************************************************************
>     
> 1)Which kind od analog filter and which sample rate you suggest me?
> 2)How many point (hence resolution or Bins like you say) I need? 3)What
> I should check for see if human being was detect? Power, Amplitude,
> Phase ??

You really haven't given enough information, so I'm going to reply with 
vague answers that will just raise more questions.

1: wide open, and fast.  My knee-jerk reaction is to think that you 
should sample at least four times faster than your 600Hz maximum 
frequency, but if you anticipate modulation that's a significant fraction 
of your 600Hz, then -- faster.  You really need to know the actual 
spectral content of the signal, and you need to know how you intend to 
decode the signal, before you can get a definitive answer.  I very much 
doubt you'll need to go over 6kHz.

2: I don't think you want to do this with an FFT.  The FFT is a small 
part of signal processing; I don't think it covers what you want to do 
here.

3: What changes the most distinctly?

> @Andrew
> Thanks for your formula on Frequency_Resolution. Moreover I have check
> my signal.It is a perfect sin(x) wave and effectively IMX() vector have
> all zero value.

If it is a sine wave that is modulated either in frequency or amplitude, 
then when you consider it _with sidebands_ it won't have zero value.

-- 
www.wescottdesign.com