# Question on channelizer

Started by November 16, 2012
```>On Monday, November 19, 2012 3:53:54 AM UTC-8, gongdori wrote:
>> ...
>>=20
>> Dale,
>>=20
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
>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
>

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

```
```On Tuesday, November 20, 2012 3:44:30 AM UTC-8, gongdori wrote:
> ...
>
> 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
```