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Polyphase Filters

Started by commsignal February 13, 2012
Hello all,
  Can someone explain to me the following in Fred Harris' book Multirate
Signal Processing for Communication Systems?

1. Chapter 6 (page 143 - Separating the Aliases): The inputs to the M-path
filter are not narrowband, and phase shift alone is insufficient to effect
the destructive cancellation over the full bandwidth of the undesired
special contributions (and the next sentence regarding time-delay
beamforming).

2. Same chpater page 146 and 147: What do these graphs mean?

Thanks a lot for your time.
I would be so grateful if someone can shed some light, even a little
explanation, on these two questions. Thank you.


>Hello all, > Can someone explain to me the following in Fred Harris' book Multirate >Signal Processing for Communication Systems? > >1. Chapter 6 (page 143 - Separating the Aliases): The inputs to the
M-path
>filter are not narrowband, and phase shift alone is insufficient to
effect
>the destructive cancellation over the full bandwidth of the undesired >special contributions (and the next sentence regarding time-delay >beamforming). > >2. Same chpater page 146 and 147: What do these graphs mean? > >Thanks a lot for your time. >
On 2/14/12 4:04 AM, commsignal wrote:
> I would be so grateful if someone can shed some light, even a little > explanation, on these two questions. Thank you. >
i don't have the book. (gasp! everybody else does!) would you mind describing your question in a manner not dependent on the book? -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Hi,

you can explain the graphs 146 and 147 from the basic definition of a
polyphase filter, a device that provides several "phases", or in other
words, delayed replicas, of a signal.

The baseline group delay in 6.18 is 8 samples (the minus sign goes into
"minus" dPhase/dOmega). Looks like a symmetric 15-tap FIR.

The group delay traces are
7.55
7.65
7.75
7.85
7.95
8.05
8.15
8.25
8.35
8.45
samples. So the filter has a baseline delay of 8 samples, plus/minus 0.5
samples, in 0.1 sample steps (10 phases).
The filter is a more or less flat lowpass up to a normalized frequency of ~
0.4 (you can reach 0.5 asymptotically, but it requires a longer and longer
filter).

In a nutshell, the basic idea of the channelizer is to alias n channels on
top of each other. Now do it n times independently, giving different linear
combinations of aliases. Add them in a suitable manner so that (n-1)
aliases cancel and only the wanted channel remains.
You obtain the linear combinations by introducing variable
fractional-sample delay with the polyphase filter. 
It causes a phase shift that depends on both the fractional delay
(polyphase branch) and the channel frequency. 
Finally, shuffle the blocks to re-order into a structure that's convenient
to implement.
>> Looks like a symmetric 15-tap FIR
make that 17 (16 delays)