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
How to interpolation in frequency domain will not affect time domain signal?
Started by ●June 30, 2009
Reply by ●July 1, 20092009-07-01
Reply by ●July 2, 20092009-07-02
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
