Edson: I recently went through all of this and I have this stuff figured out at last. The goal is: given a fixed sized FFT, what can you do to make a tone generally narrower. Let me give you some rules of thumb without resorting to math.
In <<GENERAL>> the use of a window, a standard window, is completely suboptimal in almost every way for the polyphase FFT. If your goal is strictly narrowing the width of a tone that is not in the center of an FFT bin, here is the procedure one should follow in my opinion. Suppose you have a fixed FFT size. Suppose it is 2048 points. You display the power in each bin (square magnitude or dB) and as a result, you are unhappy with the width of the tone as a result. WOLA based polyphase FFT makes use of some oversampling, signal processing mathematical processes to fix this. Suppose we want to the tone to be 5 times narrower than it is now but we will want to use the 2048 sample FFT. WOLA polyphase FFT says take 5 * 2048 samples, window the entire 5*2048 samples, break the windowed 5*2048 into five contiguous blocks of 2048 samples, overlap them into five rows and add down the five long column to produce a final 2048 samples. Give this 2048 samples to the FFT. When you do this, you will see that all tones are much narrower in your final result, producing a much clear spectrum analysis tool. All of this sounds simple, you jump in and apply a window and the results are less than perfect because you have chosen your favorite window and it does not fit the problem as Alex has said. In fact, take all window you know about, and dump them into the trash. None of them are a perfect fit for this problem. WHAT IS a nearly perfect fit is a simple low pass filter, designed by your favorite FIR design program. When you think of it this way, it even gives you another way of thinking of the spectral leakage. It is the same as aliasing! Since we are downsampling by five, we will have our cutoff for the FIR filter be 1/5 (assuming the sample rate is 1.0) and it will be a 5*2048 long filter. Use this filter as your window function and the difference in the results are remarkable. If you need more sideband suppression and you can tolerate slightly more ripple, and your are downsampling by N, bring the cutoff of the low pass inside of 1/N but NOT as far as 1/(N+1). After I figured this methodology out, I even found a reference where you can read about this in more detail. It was in the new edition (2004) of Richard Lyons "Understanding Digital Signal Processing" on page 544 under the heading "A Practical Spectrum Analyzer". He includes the basic words I have said to you here, saying that typical Windows stink and insisting that an FIR low pass with cut off at 1/N (downsampling rate) or slightly less is ideal. Until I gave up on all windows and designed a low pass filter, I did not get it until I read this text. Lyons should be on every signal processing programmer's shelf. I really want to thank Alex for shoving this in front of our noses in such a spectacular way. The impact of his Rocky software, through the sincerest form of flattery will be truly widespread and this is not the last example. Good luck, Bob N4HY Alex, VE3NEA wrote: >Hi Edson, > >Your description is correct, except that raised cosine is a poor choice of >the window function. See this article for details: >http://archive.chipcenter.com/dsp/DSP000315F1.html > >73 Alex VE3NEA > > > > > >>Does anyone know where I can find a good description for the polyphase >>fft? >> >>So far I could only find that the polyphase fft can be obtained by >>getting a block o sampled data. Let's say 4 * N where N is the FFT >>point size; window the block using a raised cosine function; >>superimpose and add the blocks and compute a fft. >> >>I would like to know if this description is accurate. >> >>Any pointer would be appreciated. >> >>73, >> >>-- Edson, n1vtn >> >> >> >> >> -- Laziness is the number one inspiration for ingenuity. Guilty as charged! ------------------------ Yahoo! Groups Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. Make Yahoo! your home page http://us.click.yahoo.com/dpRU5A/wUILAA/yQLSAA/ELTolB/TM --------------------------------------------------------------------~-> Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/soft_radio/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
