# Talk:Filter bank

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

## 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.wikipedia.org/w/index.php?title=Window_function&diff=next&oldid=225774556

http://en.wikipedia.org/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)

## 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 Kth channel, centered at frequency KB, down-converts its passband by KB hertz, meaning that it effectively multiplies the input sequence by ${\displaystyle e^{-i2\pi KB\ t},}$ where due to block processing,  ${\displaystyle t}$ is reset to 0 at the start of each block (every 256 samples). And that creates a phase discontinuity of ${\displaystyle \scriptstyle 2\pi \ K\ B\ 256\ T=\pi K}$ 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.

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. ${\displaystyle S_{k}=A_{1}\cdot e^{i2\pi ft}}$) with its spectral counterpart in channel K+1 (e.g ${\displaystyle S_{k+1}=A_{2}\cdot e^{i2\pi (f-B)t}}$).  Beginning at an arbitrary time, t1, but with oscillators starting at phase 0, the process is:

{\displaystyle {\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)