# Group Delay of Polyphase FIR filters

Started by June 10, 2004
```Could anyone explain or point me to any literature that explains how
to compute the group delays of polyphase FIR filters used for
decimation and interpolation?

For example if an FIR filter with (N*L) coefficients is implemented as
L polyphase filters each with N coefficients, what is the group delay
for the filter? Measured values indicate the group delay to be less
than (N*L)/2 which is for a single stage FIR filter with (N*L)
coefficients.

Debashis Ghosh
dghosh@datx.com
```
```The filter is equivalent to a simple FIR filter at the highest sample
rate.  The group delay can be computed at that sample rate from the simple
filter, then referred back to the lower input or output rate.

dghosh wrote:

> Could anyone explain or point me to any literature that explains how
> to compute the group delays of polyphase FIR filters used for
> decimation and interpolation?
>
> For example if an FIR filter with (N*L) coefficients is implemented as
> L polyphase filters each with N coefficients, what is the group delay
> for the filter? Measured values indicate the group delay to be less
> than (N*L)/2 which is for a single stage FIR filter with (N*L)
> coefficients.
>
>
> Debashis Ghosh
> dghosh@datx.com

--
--Ray Andraka, P.E.
President, the Andraka Consulting Group, Inc.
401/884-7930     Fax 401/884-7950
email ray@andraka.com
http://www.andraka.com

"They that give up essential liberty to obtain a little
temporary safety deserve neither liberty nor safety."
-Benjamin Franklin, 1759

```
```Thanks for the answer.

I have a 168 tap LP FIR filter implemented as a 6-phase polyphase
filter used for decimation. The sampling rate is 6KHz and the
decimated rate is 1KHz. While the frequency response is as designed,
the measured group delay at 1KHz is 20 instead of 14 (= (168/2) *
(1/6) ). What could be the source of this dicrepancy?

Debashis Ghosh
Data Translation Inc.
http://www.datatranslation.com

Ray Andraka <ray@andraka.com> wrote in message news:<40C892A7.BD717AE5@andraka.com>...
> The filter is equivalent to a simple FIR filter at the highest sample
> rate.  The group delay can be computed at that sample rate from the simple
> filter, then referred back to the lower input or output rate.
>
> dghosh wrote:
>
> > Could anyone explain or point me to any literature that explains how
> > to compute the group delays of polyphase FIR filters used for
> > decimation and interpolation?
> >
> > For example if an FIR filter with (N*L) coefficients is implemented as
> > L polyphase filters each with N coefficients, what is the group delay
> > for the filter? Measured values indicate the group delay to be less
> > than (N*L)/2 which is for a single stage FIR filter with (N*L)
> > coefficients.
> >
> >
> > Debashis Ghosh
> > dghosh@datx.com
>
> --
> --Ray Andraka, P.E.
> President, the Andraka Consulting Group, Inc.
> 401/884-7930     Fax 401/884-7950
> email ray@andraka.com
> http://www.andraka.com
>
>  "They that give up essential liberty to obtain a little
>   temporary safety deserve neither liberty nor safety."
>                                           -Benjamin Franklin, 1759
```
```Other delays in your implementation.  The part of the group delay I was referring to only
accounts for the group delay due to the filter coefficients, not to any additional delays

dghosh wrote:

>
> I have a 168 tap LP FIR filter implemented as a 6-phase polyphase
> filter used for decimation. The sampling rate is 6KHz and the
> decimated rate is 1KHz. While the frequency response is as designed,
> the measured group delay at 1KHz is 20 instead of 14 (= (168/2) *
> (1/6) ). What could be the source of this dicrepancy?
>
> Debashis Ghosh
> Data Translation Inc.
> http://www.datatranslation.com
>
> Ray Andraka <ray@andraka.com> wrote in message news:<40C892A7.BD717AE5@andraka.com>...
> > The filter is equivalent to a simple FIR filter at the highest sample
> > rate.  The group delay can be computed at that sample rate from the simple
> > filter, then referred back to the lower input or output rate.
> >
> > dghosh wrote:
> >
> > > Could anyone explain or point me to any literature that explains how
> > > to compute the group delays of polyphase FIR filters used for
> > > decimation and interpolation?
> > >
> > > For example if an FIR filter with (N*L) coefficients is implemented as
> > > L polyphase filters each with N coefficients, what is the group delay
> > > for the filter? Measured values indicate the group delay to be less
> > > than (N*L)/2 which is for a single stage FIR filter with (N*L)
> > > coefficients.
> > >
> > > Thanks in advance.
> > >
> > > Debashis Ghosh
> > > dghosh@datx.com
> >
> > --
> > --Ray Andraka, P.E.
> > President, the Andraka Consulting Group, Inc.
> > 401/884-7930     Fax 401/884-7950
> > email ray@andraka.com
> > http://www.andraka.com
> >
> >  "They that give up essential liberty to obtain a little
> >   temporary safety deserve neither liberty nor safety."
> >                                           -Benjamin Franklin, 1759

--
--Ray Andraka, P.E.
President, the Andraka Consulting Group, Inc.
401/884-7930     Fax 401/884-7950
email ray@andraka.com
http://www.andraka.com

"They that give up essential liberty to obtain a little
temporary safety deserve neither liberty nor safety."
-Benjamin Franklin, 1759

```