Hello, I'm a newbie in DSP world and got several questions on channelizer. I recently studied polyphase channelizer and weighted Overlap-add(WOLA) filter bank. It seems that the only benefit WOLA has is that the number of channels can be not related to the decimation factor. Why is it so beneficial? When each channel is moved to baseband, isn't it desirable to have the minimal sampling frequency, thus minimal number of samples? The number of channels is bounded by the size of FFT in both channelizers. If the number of channels we have is not close to any FFT size, for example 300 channels, Is it possible to use FFT based channelizer? If so, do we waste channels? Is it still more efficient than straight-forward approach in general? Thanks for your help! gongdori
Question on channelizer
Started by ●November 16, 2012
Reply by ●November 16, 20122012-11-16
On Friday, November 16, 2012 6:20:50 PM UTC-5, gongdori wrote:> Hello, > > > > I'm a newbie in DSP world and got several questions on channelizer. > > I recently studied polyphase channelizer and weighted Overlap-add(WOLA) > > filter bank. It seems that the only benefit WOLA has is that the number of > > channels can be not related to the decimation factor. Why is it so > > beneficial? When each channel is moved to baseband, isn't it desirable to > > have the minimal sampling frequency, thus minimal number of samples? > > > > The number of channels is bounded by the size of FFT in both channelizers. > > If the number of channels we have is not close to any FFT size, for example > > 300 channels, Is it possible to use FFT based channelizer? If so, do we > > waste channels? Is it still more efficient than straight-forward approach > > in general? > > > > Thanks for your help! > > > > gongdoriThere are other advantages. One in particular is reduced leakage. If you can describe what you mean by "straight-forward approach", then more pros and cons can be shared. John
Reply by ●November 17, 20122012-11-17
On Friday, November 16, 2012 3:20:50 PM UTC-8, gongdori wrote:> Hello, > ... When each channel is moved to baseband, isn't it desirable to > have the minimal sampling frequency, thus minimal number of samples? > ... > > gongdoriAs is usually the case, it depends. If you wish to preserve the spectral content of the output channels, you need to produce samples of each output channel at a high enough frequency to prevent aliasing. That is, the sample frequency must be high enough that the replicas of the baseband filter response, separated in the frequency domain by the output sample frequency, don't overlap. Dale B. Dalrymple
Reply by ●November 19, 20122012-11-19
>On Friday, November 16, 2012 6:20:50 PM UTC-5, gongdori wrote: >> Hello, >> >> >> >> I'm a newbie in DSP world and got several questions on channelizer. >> >> I recently studied polyphase channelizer and weighted Overlap-add(WOLA) >> >> filter bank. It seems that the only benefit WOLA has is that the numberof>> >> channels can be not related to the decimation factor. Why is it so >> >> beneficial? When each channel is moved to baseband, isn't it desirableto>> >> have the minimal sampling frequency, thus minimal number of samples? >> >> >> >> The number of channels is bounded by the size of FFT in bothchannelizers.>> >> If the number of channels we have is not close to any FFT size, forexample>> >> 300 channels, Is it possible to use FFT based channelizer? If so, do we >> >> waste channels? Is it still more efficient than straight-forwardapproach>> >> in general? >> >> >> >> Thanks for your help! >> >> >> >> gongdori > >There are other advantages. One in particular is reduced leakage. If youcan describe what you mean by "straight-forward approach", then more pros and cons can be shared.> >John >John, thank you for your reply. What I meant by "straight-forward approach" is the approach which filters the desired channel, shifts it to baseband and performs down-sampling, per channel.
Reply by ●November 19, 20122012-11-19
>On Friday, November 16, 2012 3:20:50 PM UTC-8, gongdori wrote: >> Hello, >> ... When each channel is moved to baseband, isn't it desirable to >> have the minimal sampling frequency, thus minimal number of samples? >> ... >>=20 >> gongdori > >As is usually the case, it depends. If you wish to preserve the spectralco=>ntent of the output channels, you need to produce samples of each outputch=>annel at a high enough frequency to prevent aliasing. That is, the samplef=>requency must be high enough that the replicas of the baseband filterrespo=>nse, separated in the frequency domain by the output sample frequency,don'=>t overlap. > >Dale B. Dalrymple >Dale, Thank you for your reply. what you talked about in your previous post is what I was not sure. If Polyphase channelizer is used, it extracts all channel, down-samples "enough" so that it can meet the Nyquist criterion. In other words, all channels are critically sampled. Thus, I am wondering what benefit we get by using WOLA channelizer, where we can have higher sampling rate in each channel. Gongdori
Reply by ●November 19, 20122012-11-19
On Monday, November 19, 2012 6:50:37 AM UTC-5, gongdori wrote:> >On Friday, November 16, 2012 6:20:50 PM UTC-5, gongdori wrote: > > >> Hello, > > >> > > >> > > >> > > >> I'm a newbie in DSP world and got several questions on channelizer. > > >> > > >> I recently studied polyphase channelizer and weighted Overlap-add(WOLA) > > >> > > >> filter bank. It seems that the only benefit WOLA has is that the number > > of > > >> > > >> channels can be not related to the decimation factor. Why is it so > > >> > > >> beneficial? When each channel is moved to baseband, isn't it desirable > > to > > >> > > >> have the minimal sampling frequency, thus minimal number of samples? > > >> > > >> > > >> > > >> The number of channels is bounded by the size of FFT in both > > channelizers. > > >> > > >> If the number of channels we have is not close to any FFT size, for > > example > > >> > > >> 300 channels, Is it possible to use FFT based channelizer? If so, do we > > >> > > >> waste channels? Is it still more efficient than straight-forward > > approach > > >> > > >> in general? > > >> > > >> > > >> > > >> Thanks for your help! > > >> > > >> > > >> > > >> gongdori > > > > > >There are other advantages. One in particular is reduced leakage. If you > > can describe what you mean by "straight-forward approach", then more pros > > and cons can be shared. > > > > > >John > > > > > > > > > John, thank you for your reply. > > What I meant by "straight-forward approach" is the approach which filters > > the desired channel, shifts it to baseband and performs down-sampling, per > > channel.For 300 channels with the same bandwidth and regular frequency spacing, you are probably better off from an efficiency standpoint with a polyphase channelizer, ignoring the channels you don't care about. If you have varying bandwidths and/or irregular spacings, then the approach described in this paper may be more appropriate: http://www.3db-labs.com/01598092_MultibandFilterbank.pdf John
Reply by ●November 19, 20122012-11-19
>On Monday, November 19, 2012 6:50:37 AM UTC-5, gongdori wrote: >> >On Friday, November 16, 2012 6:20:50 PM UTC-5, gongdori wrote: >>=20 >> >> Hello, >>=20 >> >>=20 >>=20 >> >>=20 >>=20 >> >>=20 >>=20 >> >> I'm a newbie in DSP world and got several questions onchannelizer.=20>>=20 >> >>=20 >>=20 >> >> I recently studied polyphase channelizer and weightedOverlap-add(WOLA=>) >>=20 >> >>=20 >>=20 >> >> filter bank. It seems that the only benefit WOLA has is that thenumbe=>r >>=20 >> of >>=20 >> >>=20 >>=20 >> >> channels can be not related to the decimation factor. Why is it so >>=20 >> >>=20 >>=20 >> >> beneficial? When each channel is moved to baseband, isn't itdesirable>>=20 >> to >>=20 >> >>=20 >>=20 >> >> have the minimal sampling frequency, thus minimal number of samples? >>=20 >> >>=20 >>=20 >> >>=20 >>=20 >> >>=20 >>=20 >> >> The number of channels is bounded by the size of FFT in both >>=20 >> channelizers. >>=20 >> >>=20 >>=20 >> >> If the number of channels we have is not close to any FFT size, for >>=20 >> example >>=20 >> >>=20 >>=20 >> >> 300 channels, Is it possible to use FFT based channelizer? If so, dow=>e >>=20 >> >>=20 >>=20 >> >> waste channels? Is it still more efficient than straight-forward >>=20 >> approach >>=20 >> >>=20 >>=20 >> >> in general?=20 >>=20 >> >>=20 >>=20 >> >>=20 >>=20 >> >>=20 >>=20 >> >> Thanks for your help! >>=20 >> >>=20 >>=20 >> >>=20 >>=20 >> >>=20 >>=20 >> >> gongdori >>=20 >> > >>=20 >> >There are other advantages. One in particular is reduced leakage. Ifyou>>=20 >> can describe what you mean by "straight-forward approach", then morepros>>=20 >> and cons can be shared.=20 >>=20 >> > >>=20 >> >John >>=20 >> > >>=20 >>=20 >>=20 >>=20 >>=20 >> John, thank you for your reply. >>=20 >> What I meant by "straight-forward approach" is the approach whichfilters>>=20 >> the desired channel, shifts it to baseband and performs down-sampling,pe=>r >>=20 >> channel. > >For 300 channels with the same bandwidth and regular frequency spacing,you=> are probably better off from an efficiency standpoint with a polyphasecha=>nnelizer, ignoring the channels you don't care about. If you have varyingb=>andwidths and/or irregular spacings, then the approach described in thispa=>per may be more appropriate: > >http://www.3db-labs.com/01598092_MultibandFilterbank.pdf > >John >John, Thanks a lot! That article really helped!
Reply by ●November 20, 20122012-11-20
>>On Monday, November 19, 2012 6:50:37 AM UTC-5, gongdori wrote: >>> >On Friday, November 16, 2012 6:20:50 PM UTC-5, gongdori wrote: >>>=20 >>> >> Hello, >>>=20 >>> >>=20 >>>=20 >>> >>=20 >>>=20 >>> >>=20 >>>=20 >>> >> I'm a newbie in DSP world and got several questions on >channelizer.=20 >>>=20 >>> >>=20 >>>=20 >>> >> I recently studied polyphase channelizer and weighted >Overlap-add(WOLA= >>) >>>=20 >>> >>=20 >>>=20 >>> >> filter bank. It seems that the only benefit WOLA has is that the >numbe= >>r >>>=20 >>> of >>>=20 >>> >>=20 >>>=20 >>> >> channels can be not related to the decimation factor. Why is it so >>>=20 >>> >>=20 >>>=20 >>> >> beneficial? When each channel is moved to baseband, isn't it >desirable >>>=20 >>> to >>>=20 >>> >>=20 >>>=20 >>> >> have the minimal sampling frequency, thus minimal number ofsamples?>>>=20 >>> >>=20 >>>=20 >>> >>=20 >>>=20 >>> >>=20 >>>=20 >>> >> The number of channels is bounded by the size of FFT in both >>>=20 >>> channelizers. >>>=20 >>> >>=20 >>>=20 >>> >> If the number of channels we have is not close to any FFT size, for >>>=20 >>> example >>>=20 >>> >>=20 >>>=20 >>> >> 300 channels, Is it possible to use FFT based channelizer? If so,do>w= >>e >>>=20 >>> >>=20 >>>=20 >>> >> waste channels? Is it still more efficient than straight-forward >>>=20 >>> approach >>>=20 >>> >>=20 >>>=20 >>> >> in general?=20 >>>=20 >>> >>=20 >>>=20 >>> >>=20 >>>=20 >>> >>=20 >>>=20 >>> >> Thanks for your help! >>>=20 >>> >>=20 >>>=20 >>> >>=20 >>>=20 >>> >>=20 >>>=20 >>> >> gongdori >>>=20 >>> > >>>=20 >>> >There are other advantages. One in particular is reduced leakage. If >you >>>=20 >>> can describe what you mean by "straight-forward approach", then more >pros >>>=20 >>> and cons can be shared.=20 >>>=20 >>> > >>>=20 >>> >John >>>=20 >>> > >>>=20 >>>=20 >>>=20 >>>=20 >>>=20 >>> John, thank you for your reply. >>>=20 >>> What I meant by "straight-forward approach" is the approach which >filters >>>=20 >>> the desired channel, shifts it to baseband and performs down-sampling, >pe= >>r >>>=20 >>> channel. >> >>For 300 channels with the same bandwidth and regular frequency spacing, >you= >> are probably better off from an efficiency standpoint with a polyphase >cha= >>nnelizer, ignoring the channels you don't care about. If you havevarying>b= >>andwidths and/or irregular spacings, then the approach described in this >pa= >>per may be more appropriate: >> >>http://www.3db-labs.com/01598092_MultibandFilterbank.pdf >> >>John >> > > >John, > >Thanks a lot! That article really helped! > >I am just posting it here in case this article helps you. http://link.springer.com/article/10.1007%2Fs10470-011-9746-y#page-1
Reply by ●November 20, 20122012-11-20
On Monday, November 19, 2012 3:53:54 AM UTC-8, gongdori wrote:> ... > > Dale, > > Thank you for your reply. what you talked about in your previous post is > what I was not sure. If Polyphase channelizer is used, it extracts all > channel, down-samples "enough" so that it can meet the Nyquist criterion. > In other words, all channels are critically sampled. Thus, I am wondering > what benefit we get by using WOLA chnanelizer, where we can have higher > sampling rate in each channel. > > GongdoriThe polyphase channelizer and the WOLA channalizer are examples of DFT channelizers that work by windowing a data sequence and generate subchannels with frequency response determined by the coefficients of the window. Such systems have three independent parameters when applied to streams of data: window (size and coefficients), transform size and stride. The window determines the frequency response of the channels. The transform size determines the number of channels generated (but not necessarily used). The stride is the number of samples by which the window moves along the data stream between subsequent implementations of the channelizer. The stride is the desampling ratio. The people who speak of 'critical sampling' seem to assume a rectangular window the size of the transform and a stride of the same size. This is not a necessary assumption. The difference between polyphase and WOLA channelizers is that the channelizer described as WOLA has a window longer than instead of equal to the transform size. There are applications where the rectangular window does not produce an adequate channel frequency response and so longer windows and non-unity weights may be required. The 'critical sampling' assumptions produce a channel frequency response that is a sinc function. This gives a worst-case stopband rejection of only about 13dB and a gain at adjacent channel crossover of -3.92 dB. Some applications don't find this acceptable and require larger windows to achieve greater stopband rejection or flatter gain across the channel. Application determined channel responses can require strides with values smaller than the transform size (smaller desampling) to prevent significant aliasing. Dale B. Dalrymple
Reply by ●November 20, 20122012-11-20
>On Monday, November 19, 2012 3:53:54 AM UTC-8, gongdori wrote: >> ... >>=20 >> Dale, >>=20 >> Thank you for your reply. what you talked about in your previous postis>> what I was not sure. If Polyphase channelizer is used, it extracts all >> channel, down-samples "enough" so that it can meet the Nyquistcriterion.>> In other words, all channels are critically sampled. Thus, I amwondering>> what benefit we get by using WOLA chnanelizer, where we can have higher >> sampling rate in each channel. >>=20 >> Gongdori > >The polyphase channelizer and the WOLA channalizer are examples of DFTchan=>nelizers that work by windowing a data sequence and generate subchannelswi=>th frequency response determined by the coefficients of the window. Suchsy=>stems have three independent parameters when applied to streams of data:wi=>ndow (size and coefficients), transform size and stride. The windowdetermi=>nes the frequency response of the channels. The transform size determinest=>he number of channels generated (but not necessarily used). The stride ist=>he number of samples by which the window moves along the data streambetwee=>n subsequent implementations of the channelizer. The stride is thedesampl=>ing ratio. > >The people who speak of 'critical sampling' seem to assume a rectangularwi=>ndow the size of the transform and a stride of the same size. This is nota=> necessary assumption. The difference between polyphase and WOLAchannelize=>rs is that the channelizer described as WOLA has a window longer thaninste=>ad of equal to the transform size. > >There are applications where the rectangular window does not produce anade=>quate channel frequency response and so longer windows and non-unityweight=>s may be required. The 'critical sampling' assumptions produce a channelfr=>equency response that is a sinc function. This gives a worst-case stopband=>rejection of only about 13dB and a gain at adjacent channel crossover of-3=>.92 dB. Some applications don't find this acceptable and require largerwin=>dows to achieve greater stopband rejection or flatter gain across thechann=>el. Application determined channel responses can require strides withvalue=>s smaller than the transform size (smaller desampling) to preventsignifica=>nt aliasing. > >Dale B. Dalrymple >Dale, Thank you so much for your informative reply. There was one thing I was not sure about in your reply and that was the part you mentioned about rectangular window. Assuming we have polyphse- channelizer, which outputs critically-sampled channel data, I don't understand why it has only 13 dB separation. Doesn't it depend on the filter which is realized as polyphase structure? In frequency domain channelization where data is transformed to frequency domain and only the channel of interested is selected and converted back to time-domain by performing IFFT, I understand that it would suffer from rectangular windowing and sinc roll-off. If what you meant was the frequency domain channelization, is there any technique we can use to efficiently compensate the roll off? Gogndori
