Talk:Filter bank

Untitled

Should give examples of some popular filter banks, and also talk about perfect reconstruction.

Perfect reconstruction is noted (at an encyclopedic level) in section § FFT filter banks.

I don't know that there is such a thing as a "popular" filter bank, unless you mean WOLA, which is already included.

--Bob K (talk) 23:56, 3 February 2023 (UTC)

Stub tag

I'm putting a stub tag to this article. There are many volumes of books on filter banks, and filter banks are being used in virtually every signal processing application nowadays.--C6H12O6 11:06, 30 November 2006 (UTC)

Errata

We say "A filter bank is an array of band-pass filters". But bandpass filters produce bandpass outputs, which are not down-converted and decimated. But many structures called "filter banks" also do the down-conversion. And subsequent synthesis algorithms must include upconversion.

We also say "With the polyphase matrix you easily answer the question for the perfect reconstruction property of a filter bank." That doesn't appear to be a correct English sentence. Besides that, I don't think it is a correct statement, because of the important detail of the design of the analysis and synthesis filters.

--Bob K (talk) 21:15, 14 September 2009 (UTC)

fredric j harris

User:spinningspark wrote: "I'm sure he uses capitalization"

So here is the actual book cover image

--Bob K (talk) 23:37, 13 December 2009 (UTC)

That is beside the point, it is still not the proper way to format a citation. SpinningSpark 19:43, 16 December 2009 (UTC)

No, that's a different point. The point is whether or not fred harris "uses capitalization". Here's another counter-example: http://electrical.sdsu.edu/faculty/frederick_harris.html And I can scan the title pages inside the book, if you like.

As to your next point, check out these edits by other editors:

http://en.wiki.x.io/w/index.php?title=Window_function&diff=next&oldid=225774556

http://en.wiki.x.io/w/index.php?title=Window_function&action=historysubmit&diff=295853906&oldid=295793664

--Bob K (talk) 22:52, 16 December 2009 (UTC)

Ok, I surrender. SpinningSpark 01:30, 17 December 2009 (UTC)

Multidimensional Filter Bank Design

Potentially a good addition to the article. But chock full of errors. Not up to Wikipedia standards. Here are some examples:

• It has a wide application prospect, researches in this area are very important when people try to get insight to the multidimensional signal. (punctuation)

• Also filters can be used both in one dimensional signal processing and multidimensional signal processing; and by processing the signal, we can get one or more certain kinds of signal that may be used under different kinds of conditions. (doesn't say anything useful)

• In recent decades, sub-band handing becomes more and more popular in some fields like image & video processing, communication and so on. (verb tense)

• However, many of signals mentioned before are hi-dimensional, which ask for the well design of hi-dimensional filter banks. (various problems)

And those are just the first paragraph, of many.

• Oversampled filter banks are multirate filter banks where the number of channels is larger than the sampling rate.

I assume this is trying to say that the more channels you have, the less bandwidth per channel, and the lower the Nyquist rate. So a fixed sample rate will exceed Nyquist above some minimum number of channels. But "number of channels" and "sampling rate" are quantities with different units.

And so on.

--Bob K (talk) 13:06, 15 November 2013 (UTC)

How does the Nyquist sampling criteria constitute the difference between a filter bank and a spectrum analyzer?

The line "the Nyquist sampling criteria (which is what distinguishes a filter bank from a spectrum analyzer)." seems a bit cryptic to the uninitiated (which includes myself), is it possible to elaborate in the article? Norlesh (talk) 04:20, 14 August 2014 (UTC)

It is now explained in the article, although maybe not at the time of your request. Briefly, you can recover the original signal from a filter bank, but not from a spectrum analyzer. Hope that helps! --Bob K (talk) 00:41, 14 June 2021 (UTC)

Subtleties in need of a reference

While waiting for an oil change yesterday, I entertained myself with the question of inadvertent phase discontinuities that may occur at the block boundaries of an FFT-based bank of receivers. For instance, consider a complex-valued data-sequence sampled at intervals of T seconds and divided into 512 channels. The corresponding channel spacing and bandwidth is B = 1/(512•T). And suppose the desired output sample-rate per channel is 2B (referred to as oversampled or underdecimated). To achieve that rate, the FFTs must be performed at intervals of 256 samples. The K^th channel, centered at frequency KB, down-converts its passband by KB hertz, meaning that it effectively multiplies the input sequence by $e^{-i2\pi KB\ t},$ where due to block processing,  $t$ is reset to 0 at the start of each block (every 256 samples). And that creates a phase discontinuity of $\scriptstyle 2\pi \ K\ B\ 256\ T=\pi K$ at every block boundary. For even numbered channels, the discontinuity is a multiple of 2π, which is not a discontinuity. But odd numbered channels will experience a sign inversion at every boundary.

Since writing that naïve comment 7 years ago, I discovered the WOLA algorithm, which probably prevents the discontinuity I was worried about. But there still might be a synthesis issue (below). --Bob K (talk) 19:07, 13 June 2021 (UTC)

There is also a subtle issue when recombining (synthesizing) multiple over-sampled channels, and expecting the overlap regions to add constructively (in-phase). It can be demonstrated by the process of recombining a down-converted sinusoid in channel K (e.g. $S_{k}=A_{1}\cdot e^{i2\pi ft}$) with its spectral counterpart in channel K+1 (e.g $S_{k+1}=A_{2}\cdot e^{i2\pi (f-B)t}$).  Beginning at an arbitrary time, t₁, but with oscillators starting at phase 0, the process is:

${\begin{aligned}S_{k}\cdot e^{i2\pi KB(t-t_{1})}+S_{k+1}\cdot e^{i2\pi (K+1)B(t-t_{1})}&=e^{i2\pi KB(t-t_{1})}\cdot [S_{k}+S_{k+1}\cdot e^{i2\pi B(t-t_{1})}]\\&=e^{i2\pi KB(t-t_{1})}\cdot e^{i2\pi ft}\cdot [A_{1}+A_{2}\cdot e^{-i2\pi Bt_{1}}]\\&=e^{i2\pi (KB+f)t}\cdot e^{-i2\pi KBt_{1}}\cdot [A_{1}+A_{2}\cdot e^{-i2\pi Bt_{1}}]\end{aligned}}$

The condition for A₁ and A₂ to add constructively is B•t₁ = integer (n). Equivalently, t₁ = n/B = n•(512 T) = 2n•(256 T).  (256•T) is the interval between channel-samples (in the over-sampled case). So the condition for synthesis with oscillators that start at zero phase is that it begin on an even-numbered (2n) channel-sample.

I don't happen to have a handy reference for this analysis, since I did it myself, but perhaps someone else does. As far as I know (correct me if I'm wrong), these subtleties are not yet mentioned in the article, which seems like a significant omission.
--Bob K (talk) 00:55, 22 December 2014 (UTC)--

Could someone write about how Convolution Neural Networks are related to filter banks? I think a CNN is a filter bank?

121.83.16.187 (talk) 04:18, 18 May 2016 (UTC)

India Education Program course assignment

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The above message was substituted from {{IEP assignment}} by PrimeBOT (talk) on 19:58, 1 February 2023 (UTC)