What is Z^-1 in Costas Loop for BPSK?

[ultraviolet_ray]

Hi there ,
I am trying to implement a Digital Costas loop fot the demodulation of a BPSK signal in MATLAB. I even found a thread related , at the following linkhttps://www.edaboard.com/threads/145812/
The related document from where I studied is**broken link removed**

I am confused about this Z^-1 . Is this a simple delay ? If so what value should I initially assume ,if I am taking my first sample value?

Waiting for an early response.

 

[zorro]

Re: Costas Loop for BPSK

Z^-1 means a delay of one sample in a discrete-time (sampled) system.

If so what value should I initially assume ,if I am taking my first sample value?

This is the initial condition of the problem. It can have any value. For a complete solution you should know it, because the initial transient depends of initial conditions.
Nevertheless, the steady state does not depend of initial conditions (if the system is stable).

Regards

Z