A question about DFT

On Mar 22, 11:03&#4294967295;pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:

> > Well I understand it as a property of the designed system. If a radar
> > uses only narrowband signals it can not achieve a superior range
> > resolution.
>
> GPS uses ~10 MHz wide signal however there are receivers which achieve
> sub-centimeter resolution.

That may be where our fundamental definitions disagree. I would call
the error in the measurement the "accuracy". If you are trying to
estimate the frequency then the SNR plays an important roll. The terms
accuracy and resolution are often confused.

The  original poster explicitly mentioned the use of the DFT for the
detection of the sinusoids.- he wasn't interested in estimating the
frequencies - atleast not yet.

Consider a radar system. Resolution gives you the ability to  tell
that there are 3 aircraft heading you're way. Not one, not two, but
three. Accuracy is the ability of the system to tell you that an
aircraft is 20.0345 km away (with some variance). The 2 capabilities
are very different. However, in the presence of additional aircraft
the accuracy the system tends to degrade.


>
> > But I think I understand your definition now. The resolution you specify
> > is the one which could be reached by a "perfect" estimation. Something
> > like a Cramer-Rao bound?
>
> Good example.
>

The CRLB deals with the limit on the variance  or how accurately you
can determine a quantity. It is not resolution. Also the CRLB is tied
with the algorithm you use to determine the quantity. If you use a
different algorithm you get a different CRLB.

Cheers,
Dave

Dave <dspguy2@netscape.net> wrote:

(snip, someone wrote)
>> GPS uses ~10 MHz wide signal however there are receivers which achieve
>> sub-centimeter resolution.
 
> That may be where our fundamental definitions disagree. I would call
> the error in the measurement the "accuracy". If you are trying to
> estimate the frequency then the SNR plays an important roll. The terms
> accuracy and resolution are often confused.

(snip)
> Consider a radar system. Resolution gives you the ability to  tell
> that there are 3 aircraft heading you're way. Not one, not two, but
> three. Accuracy is the ability of the system to tell you that an
> aircraft is 20.0345 km away (with some variance). The 2 capabilities
> are very different. However, in the presence of additional aircraft
> the accuracy the system tends to degrade.

That sounds right to me, but note that you can also ask the same
questions in transform (frequency) space.  That is, frequency
resolution and frequency accuracy.  Sometimes both at the same time.
(Note that radar uses the frequency of the return signal to determine
the speed of the object.)

-- glen