On Tuesday, November 20, 2012 3:44:30 AM UTC-8, gongdori wrote:
> ...
>
> 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?
The fourier transform of the window is the filter realized by DFT channelizers. If the window coefficients are all 1.0, the frequency response is a sinc.
> 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.
In the DFT channelizers, the DFT outputs are interpreted as time domain samples. Each DFT produces one time domain sample for each channel.
In the DFT/weight/IFFT filter structure as in the IEEE SP Mag article john referenced, you get an additional filter effect from the coefficients you apply to the DFT outputs you select for each IFFT. If you didn't explicitly apply a coefficient, the coefficient value you have selected is 1.0. You can't operate on only a finite block of data without that block selection being a window.
>
> If what you meant was the frequency domain channelization, is there any
> technique we can use to efficiently compensate the roll off
>
> Gogndori
For the DFT channelizer, you can choose a different window size and different window coefficient values to get a response different from the sinc. For the DFT/weight/IFFT filter structure you get an additional opportunity to modify the output frequency response when you select the frequency domain weights (and, of course, another place to create aliasing if you aren't careful).
Dale B. Dalrymple
Reply by gongdori●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 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.
>>=20
>> Gongdori
>
>The polyphase channelizer and the WOLA channalizer are examples of DFT
chan=
>nelizers that work by windowing a data sequence and generate subchannels
wi=
>th frequency response determined by the coefficients of the window. Such
sy=
>stems have three independent parameters when applied to streams of data:
wi=
>ndow (size and coefficients), transform size and stride. The window
determi=
>nes the frequency response of the channels. The transform size determines
t=
>he number of channels generated (but not necessarily used). The stride is
t=
>he number of samples by which the window moves along the data stream
betwee=
>n subsequent implementations of the channelizer. The stride is the
desampl=
>ing ratio.
>
>The people who speak of 'critical sampling' seem to assume a rectangular
wi=
>ndow the size of the transform and a stride of the same size. This is not
a=
> necessary assumption. The difference between polyphase and WOLA
channelize=
>rs is that the channelizer described as WOLA has a window longer than
inste=
>ad of equal to the transform size.
>
>There are applications where the rectangular window does not produce an
ade=
>quate channel frequency response and so longer windows and non-unity
weight=
>s may be required. The 'critical sampling' assumptions produce a channel
fr=
>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 larger
win=
>dows to achieve greater stopband rejection or flatter gain across the
chann=
>el. Application determined channel responses can require strides with
value=
>s smaller than the transform size (smaller desampling) to prevent
significa=
>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
Reply by gongdori●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 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.
>>=20
>> Gongdori
>
>The polyphase channelizer and the WOLA channalizer are examples of DFT
chan=
>nelizers that work by windowing a data sequence and generate subchannels
wi=
>th frequency response determined by the coefficients of the window. Such
sy=
>stems have three independent parameters when applied to streams of data:
wi=
>ndow (size and coefficients), transform size and stride. The window
determi=
>nes the frequency response of the channels. The transform size determines
t=
>he number of channels generated (but not necessarily used). The stride is
t=
>he number of samples by which the window moves along the data stream
betwee=
>n subsequent implementations of the channelizer. The stride is the
desampl=
>ing ratio.
>
>The people who speak of 'critical sampling' seem to assume a rectangular
wi=
>ndow the size of the transform and a stride of the same size. This is not
a=
> necessary assumption. The difference between polyphase and WOLA
channelize=
>rs is that the channelizer described as WOLA has a window longer than
inste=
>ad of equal to the transform size.
>
>There are applications where the rectangular window does not produce an
ade=
>quate channel frequency response and so longer windows and non-unity
weight=
>s may be required. The 'critical sampling' assumptions produce a channel
fr=
>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 larger
win=
>dows to achieve greater stopband rejection or flatter gain across the
chann=
>el. Application determined channel responses can require strides with
value=
>s smaller than the transform size (smaller desampling) to prevent
significa=
>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
Reply by dbd●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.
>
> Gongdori
The 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 commsignal●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 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,
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 have
varying
>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!
>
>
>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 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, 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 have varying
b=
>andwidths and/or irregular spacings, then the approach described in this
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 gongdori●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 spectral
co=
>ntent of the output channels, you need to produce samples of each output
ch=
>annel at a high enough frequency to prevent aliasing. That is, the sample
f=
>requency must be high enough that the replicas of the baseband filter
respo=
>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 gongdori●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 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.
Reply by dbd●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?
> ...
>
> gongdori
As 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