Timeline for Leakage in power spectral density estimation
Current License: CC BY-SA 4.0
30 events
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| S Apr 13, 2020 at 14:10 | history | mod moved comments to chat | |||
| S Apr 13, 2020 at 14:10 | comment | added | Peter K.♦ | Comments are not for extended discussion; this conversation has been moved to chat. Please continue any more discussion in the chat room. | |
| Apr 13, 2020 at 8:37 | comment | added | Dsp guy sam | agree :-) Thanks! | |
| Apr 13, 2020 at 8:36 | comment | added | dsp_user | @Dsp guy sam, yes, windows do matter and I did mention that in my answer. So perhaps what this discussion really comes down to is , everything else being equal, frequencies that are an exact multiple of the frequency resolution will produce a sharper peak than if we're dealing with frequencies that are located somewhere between bins. Let's leave it at that :) | |
| Apr 13, 2020 at 8:35 | vote | accept | Dsp guy sam | ||
| Apr 13, 2020 at 8:29 | comment | added | Dsp guy sam | sure, but there is still the dount in my mind if the Fc is an integral multiple of frequency resolution, does the window shape and length decide whether it fits into the bin or not? This is what this reputbale text says: Heinzel G., et al. - Spectrum and spectral density estimation by the DFT, including a comprehensive list of window functions and some new flat-top windows | |
| Apr 13, 2020 at 8:22 | comment | added | dsp_user | @Dsp guy sam, so use a window that fits in a single bin. The rectangular window produces the narrowest main lobe at the expanse of the higher noise floor. Also, don't use any overlapping to reduce the effect of windowing as much as possible. | |
| Apr 13, 2020 at 8:09 | comment | added | Dsp guy sam | I have went all the way upto 4Hz frequency resolution. I think the issue is that the estimated PSD is nothing but convolution of PSD of the sinuoid (mainly an impulse at Fc=320Hz) and the magnitude squared of the window FFT. When this convolution happens in this frequency bin then since the main lobe doesnt fit into 1 bin(for hamming window) hence it spills out even for frequency at centre of the bin. Since convolution with impulse mainly places the spectrum of the window at the centre of frequency bin which doesnt fit in it | |
| Apr 13, 2020 at 8:03 | comment | added | dsp_user | @Dsp guy sam, But this could be due to the FFT computation (and the windowing as well) producing round-off errors so your main lobe won't be exactly one thin line. Having a better frequency resolution will help resolve this, won't it? | |
| Apr 13, 2020 at 8:00 | comment | added | Dsp guy sam | I dont see the sidelobes I just dont see the main lobe fitting into the frequency bin even when the carrier frequency is centered at the bin | |
| Apr 13, 2020 at 7:59 | comment | added | dsp_user | @Dsp guy sam, can you show us those distinct side lobes that you're seeing? | |
| Apr 13, 2020 at 7:59 | comment | added | Dsp guy sam | my point is that resolution of "representation" is decided by sampling frequency and FFT size, however resolution of "resolving" frequency is decided by window main lobe, as long as window main lobe does not fit into the representation resolution, there will be spilling into adjacent bins, even if the frequency is centered at the frequency bin as in this case. | |
| Apr 13, 2020 at 7:56 | comment | added | Dsp guy sam | The waveform frequency is 320Hz. I think having the same size of FFT and window should be no restriction to verify that if a sinusoid Frequency is exactly at the center of a frequency bin, it still spills out. More overlap is required to decrease the variance of the estimate, I don't see any issue with variance being high in these plots. Anyway that still doesn't solve the resolution problem Also hampers independence of windowed sections.I have also tried resolution down to 4Hz, still the spectrum spills to nearby bins. | |
| Apr 13, 2020 at 7:33 | comment | added | dsp_user | Also, I don't see any distinct side lobes in your graph. It's still one wider main lobe. | |
| Apr 12, 2020 at 20:39 | comment | added | Dsp guy sam | any thoughts on the new findings I list in the comments above and EDIT segment of the question | |
| Apr 10, 2020 at 22:30 | comment | added | Dsp guy sam | @ dsp_user For the time being I have re-opened the question to welcome thoughts on this. | |
| Apr 10, 2020 at 22:23 | comment | added | Dsp guy sam | I have added an EDIT section in the question, it seems what we concluded here regarding the sinusoid fitting entirely within a bin if the frequency of sinusoid is an exact multiple of the resolution doesnt follow the simulations. This is exactly what i simulated but there is still leakage in the adjacent bins, details in the question added with MATLAB code. Let me know of your thoughts on this. It looks to me that the window still decides the leakage even for frequencies centered at the bins | |
| Apr 10, 2020 at 19:18 | history | edited | dsp_user | CC BY-SA 4.0 |
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| Apr 10, 2020 at 17:17 | vote | accept | Dsp guy sam | ||
| Apr 10, 2020 at 22:28 | |||||
| Apr 10, 2020 at 17:17 | comment | added | Dsp guy sam | Thanks for the explanation | |
| Apr 10, 2020 at 17:09 | comment | added | dsp_user | @Dsp guy sam, you'll still get a single peak, because your sinusoid will fit perfectly within that rectangular window (this is easy to visualize). | |
| Apr 10, 2020 at 17:06 | comment | added | Dsp guy sam | let's suppose I just have sinusoid that maps exactly at the centre of a bin. So would the bins adjacent to this bin show amplitudes? Suppose I am using a rectangular window which is known to have higher side lobes | |
| Apr 10, 2020 at 17:02 | comment | added | dsp_user | @Dsp guy sam, In a sense, but note that windowing will not add spectral leakage if the frequency is just right. it will only affect the amplitude somewhat. | |
| Apr 10, 2020 at 16:58 | comment | added | Dsp guy sam | Thanks for the answer, So we could say that there are two sources of spectral leakage, one is the resolution itself (defined by the sampling frequency and FFT size) the other is the window shape and size. So even if a frequency is indeed at exactly the centre of a bin it could still leak into other bins because of the spectral leakage of the window. Is this understanding correct. | |
| Apr 10, 2020 at 16:56 | vote | accept | Dsp guy sam | ||
| Apr 10, 2020 at 16:56 | |||||
| Apr 10, 2020 at 16:48 | comment | added | dsp_user | @Dsp guy sam, I've updated my answer. | |
| Apr 10, 2020 at 16:47 | history | edited | dsp_user | CC BY-SA 4.0 |
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| Apr 10, 2020 at 13:06 | comment | added | Dsp guy sam | Or could it be that in essence the windowing operation is a convolution of the actual signal PSD with the magnitude sqaured window, when the window is exactly the centre of the frequency bin it's main lobe is contained entirely in the bin,however anything off the centre and the main lobe itself is not contained in the bin and hence the spilling to other bins? | |
| Apr 10, 2020 at 12:57 | comment | added | Dsp guy sam | But each bin also has a range of frequencies if we talk about the power spectral density in the continuous frequencies, (digital or analog frequency), then why would say a freuency very near the centre of centre of a frequency bin produce the spectral leakage, is it because we don't actually have a real calculated estimate for this nearby freuency? And hence it is approximated which has an inherent roll off? | |
| Apr 10, 2020 at 10:37 | history | answered | dsp_user | CC BY-SA 4.0 |