# Group Delay of Multirate multistage system

Started by August 20, 2012
```Hi all,

I have an input signal with 1.5 Mhz sampling rate.
I have a serial of FIR filters which are used to interpolate this  signal.
The first filter interpolate the signal by 2 which works on 3 Mhz, the
second one interpolate the signal by 1.5 which work on 4.5 Mhz.

Could you tell me please how can I calculate the group delay of the overall
system.

I have an idea so that I can calculate the overall transfer function of the
system than calculate the group delay of the overall system. But I am not
sure if that way is right because I have two filter which they running with
different sampling frequency?

does  any one have another idea? do you think the calculation which I do to
calculate the group delay is right?

RDDSP

```
```Hi,

you'd calculate it for each stage at its respective rate.

Or: take an impulse [1 0 0 0 0 ...] sequence, run it through your chain.
Use enough samples so you get zeros at the end (it's FIR, after all).
Then use Matlab's groupdelay() function on the resulting impulse response.
Which is the impulse response for the whole chain.

The result is in units of samples at the output rate.

```