Model delays in z-domain

What would be the best way to describe the following in using
discrete-time Z transfer function:

A software loop filter computes a set of metrics using a block of data
of 1024 samples (4 samples spans a symbol period). The computed metrics
are then applied to the input data samples starting from next block,
and so on and so forth.
If I want to model this behavior in Z-domain, what would be the delay
of 1024 samples be modeled as? Z^-1024 ? Z^1024/4 (in symbol terms)?,
or Z^-1?

Jamake wrote:

> What would be the best way to describe the following in using
> discrete-time Z transfer function:
> 
> A software loop filter computes a set of metrics using a block of data
> of 1024 samples (4 samples spans a symbol period). The computed metrics
> are then applied to the input data samples starting from next block,
> and so on and so forth.
> If I want to model this behavior in Z-domain, what would be the delay
> of 1024 samples be modeled as? Z^-1024 ? Z^1024/4 (in symbol terms)?,
> or Z^-1?
> 
It really depends on what you're trying to find out.

If I read you correctly you update the metrics once every block, and I 
assume that the effect of the computed metrics on the input data isn't 
known until the end of the next block.

If that's the case, then you would use z^-1.

If you're updating symbol-by-symbol, then you'd need to use z^-256.

If you're updating sample-by-sample, then you'd need to use z^-1024.

-- 

Tim Wescott
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