On Jul 1, 9:20=A0am, "coly" <wolon...@gmail.com> wrote:
> But what puzzled me is that my interpolation method in the spectrum leads
> to a distorted time data. I want to know why.
There are many different interpolation methods. You can zero pad
things, fit parabolas to the data, use a zoom technique, etc. You
could use the DFT or inverse DFT to compute as many millions of time
or frequency domain points as you want. One of the nice things about
the DFT or IDFT is that you can use fractional values of 'n' (time
index) and 'k' (frequency index).
But no matter how you go about it, you're going to have the same
fundamental problem. Let me see if I can explain it in the following
way. Astronomers routinely capture millions of data points and do
FFTs on them. They also understand that they can express what the FFT
is doing as an N equation, N known and N unknown type of problem,
where N is in the millions.
Now suppose you said to them: "I can take 100 data points in time, FFT
it to get 100 frequency domain points, then zoom interpolate my 100
frequency domain points to create a million points. Then I can inverse
transform to obtain a million points in the time domain. So you
wouldn't have to get millions of samples, just 100 of them."
They=92ll probably think many things about that kind of statement, none
of them good, and all of them reflecting badly on the person making
the statement. But, being polite, they might just say: "But that
makes no sense at all. We have a million knowns (our million data
samples), and we need to solve for a million unknowns (a million
frequency domain points). It's mathematically impossible to solve for
a million unknowns when all we have is 100 knowns, unless we impose
some ridiculous assumptions on our signal processing model to reduce
the million unknowns down to 100."
So just imagine that you actually had the million point astronomy
input data. Pick any 100 of those points you want, and do whatever
interpolating you wish and try to =91create=92 or 'estimate' all those
other points from your interpolation scheme. Can you begin to
appreciate now why your interpolated results will have errors when
compared to the actual data? Unless you can impose some extraordinary
assumptions to simplify the problem, it=92s an impossible task no matter
what interpolation technique you use.
As Rune pointed out, you can use other methods, such as frequency
estimation. Basically, you=92d be using a different signal processing
model to obtain the needed information from the available data.
Kevin McGee
Reply by kevin●July 1, 20092009-07-01
On Jul 1, 10:33�am, Jerry Avins <j...@ieee.org> wrote:
> kevin wrote:
> � �...
> > You're starting with the incorrect premise that zero padding will make
> > up for a too short sampling interval. �It won't.
>
> That was succinct (as short as possible, but not shorter) and
> articulate. Do you write professionally?
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������
Hi Jerry:
I guess you could say so. I was an E.E. at a Navy lab for 22 years,
and published a bit through IEEE. But most of what I published was in
the form of internal documents (some 50+ reports). The vast majority
of them were restricted in some way, either by being classified or
tagged with the 'Government use only' label.
There were a lot of other things, like trip reports after attending
reviews of research programs, or sarcastic memos after the purchasing
department took 3 months to buy an Altera FPGA programmer - something
I could have done in an afternoon. Typical stuff.
I've always liked reading, and appreciate a well written book or
article. A lot of technical stuff falls into the 'whew! that was a
tough one' category. But every now and then you come across gems like
Shannon's earliest papers on Information Theory. I'm still amazed at
how clearly he described channel capacity.
Now if I can only get that division thing figured out :)
Kevin McGee
Reply by Jerry Avins●July 1, 20092009-07-01
kevin wrote:
...
> You're starting with the incorrect premise that zero padding will make
> up for a too short sampling interval. It won't.
That was succinct (as short as possible, but not shorter) and
articulate. Do you write professionally?
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by coly●July 1, 20092009-07-01
Maybe I have not discribed clearly.
I agree with you all that zero-padding doesn't improve the resolution of a
spectrum.
But what puzzled me is that my interpolation method in the spectrum leads
to
a distorted time data. I want to know why. Firstly, I discribe my
interpolation method as follows, similar to zooming out operation. Can you
depict what the time domain data like after this interpolation.
----------------------------------------------------------------------------
I interpolate the spectrum
from N points(x(n), 0<= n < N) to M (y(n), 0<= n < M) points and M > N.
the
interpolation method used is similar to zooming out a vectro graphics, I
use
y(k) = x(floor(k*N/M))*(abs(k-ceil(k*N/M))) + x(ceil(k*N/M))*(abs(k-
floor(k*N/M))).
-----------------------------------------------------------------------------
Thank you again for reply.
Reply by Rune Allnor●July 1, 20092009-07-01
On 1 Jul, 11:28, "coly" <wolon...@gmail.com> wrote:
> Maybe I have not discribed clearly.
>
> I agree with you all that zero-padding doesn't improve the resolution of a
> spectrum.
>
> But what puzzled me is that my interpolation method in the spectrum leads
> to
> a distorted time data. I want to know why.
I don't understand what you mean? If you manipulate
the spectrum and then transform this manipulated
spectrum back to time domain, you would expect some
changes compared to the original data.
If you allow for this, then keep in mind that any
interpolation routine is imperfect and introduces
artifacts. Maybe that's what you see?
Rune
Reply by coly●July 1, 20092009-07-01
Maybe I have not discribed clearly.
I agree with you all that zero-padding doesn't improve the resolution of a
spectrum.
But what puzzled me is that my interpolation method in the spectrum leads
to
a distorted time data. I want to know why. Firstly, I discribe my
interpolation method as follows, similar to zooming out operation. Can you
depict what the time domain data like after this interpolation.
----------------------------------------------------------------------------
I interpolate the spectrum
from N points(x(n), 0<= n < N) to M (y(n), 0<= n < M) points and M > N.
the
interpolation method used is similar to zooming out a vectro graphics, I
use
y(k) = x(floor(k*N/M))*(abs(k-ceil(k*N/M))) + x(ceil(k*N/M))*(abs(k-
floor(k*N/M))).
-----------------------------------------------------------------------------
Thank you again for reply.
Reply by coly●July 1, 20092009-07-01
Maybe I have not discribed clearly.
I agree with you all that zero-padding doesn't improve the resolution of a
spectrum.
But what puzzled me is that my interpolation method in the spectrum leads
to
a distorted time data. I want to know why. Firstly, I discribe my
interpolation method as follows, similar to zooming out operation. Can you
depict what the time domain data like after this interpolation.
----------------------------------------------------------------------------
I interpolate the spectrum
from N points(x(n), 0<= n < N) to M (y(n), 0<= n < M) points and M > N.
the
interpolation method used is similar to zooming out a vectro graphics, I
use
y(k) = x(floor(k*N/M))*(abs(k-ceil(k*N/M))) + x(ceil(k*N/M))*(abs(k-
floor(k*N/M))).
-----------------------------------------------------------------------------
Thank you again for reply.
Reply by coly●July 1, 20092009-07-01
Maybe I have not discribed clearly.
I agree with you all that zero-padding doesn't improve the resolution of a
spectrum.
But what puzzled me is that my interpolation method in the spectrum leads
to
a distorted time data. I want to know why. Firstly, I discribe my
interpolation method as follows, similar to zooming out operation. Can you
depict what the time domain data like after this interpolation.
----------------------------------------------------------------------------
I interpolate the spectrum
from N points(x(n), 0<= n < N) to M (y(n), 0<= n < M) points and M > N.
the
interpolation method used is similar to zooming out a vectro graphics, I
use
y(k) = x(floor(k*N/M))*(abs(k-ceil(k*N/M))) + x(ceil(k*N/M))*(abs(k-
floor(k*N/M))).
-----------------------------------------------------------------------------
Thank you again for reply.
Reply by Rune Allnor●July 1, 20092009-07-01
On 1 Jul, 04:02, "coly" <wolon...@gmail.com> wrote:
> Hi, everyone!
>
> I am new in this group. a N-point spectrum was obtained after FFT to
> N-point sampled sine signal. But the sampling frequency is not big enough
> to distinguish close peaks, I try to interpolate in the N-point spectrum to
> achieve a 2N-point spectrum which will increase resolution.
Technically speaking, you want to do zero-padding in time
domain to get narrower bin-widths in the frequency domain.
However, this does not solve what seems to be your main
problem, separating two narrow peaks in the spectrum.
The only way you can do tha by means of DFTs is to increase
the amount of actual data before computing the DFT.
Zero-padding doesn't help, as it odes not introduce new
information into the signal.
Increasing the sampling frequency odesn't help, as the
information added by sampling the timne signal denser
is spent on computing spectrum coefficients in higher
frequency bands.
You need more data samples to resolve the peaks.
Or you might try frequency estimators.
Rune
Reply by kevin●July 1, 20092009-07-01
Correction:
Consider a time domain signal. If you have 2 sine waves in an input,
say at f = 1 cps and another at f = 1.1 cps, then you can only
distinguish the 2 in the frequency domain if your frequency spacing
of
FFT outputs is sample rate/N = .1 OR LESS. Equivalently, you have to
make your sampling interval N/sample rate = 1/.1 = 10 sec. OR LONGER.
One of these days I'll learn to divide properly.
Kevin