issues with sampling rate in Giga Hertz : array exceeds maximum array size preference array exceeds maximum array size preference.

I would like to model a unit step function of a digital system with sampling clock running at 1 GHz. My undertanding is sampling rate in matlab is specified in Hertz. So, for 1 GHz sampling rate if I exceute the below,, I get the message and matlab is unresponsive . How can I model a 1GHz system sampling rate (or) can I accomplish the sane with Fs=1 Hz and still accurately model the digital system running at 1 GHz clock?

Fs = 1000000000;   %sampling rate in hertz ( 10 power 9 = Giga Hertz)
 Ts = 1/Fs; %sampling time interval in seconds
  t = 0:Ts:1000-Ts; %sampling period
 unitstep = t>=1;
 plot (t, unitstep);

Requested 1000000000000x1 (7450.6GB) array exceeds maximum array size preference array exceeds maximum array size preference. Creation of arrays greater than this limit may take a long time and cause MATLAB to become unresponsive. See array size limit or preference panel for more information.

[Walter Roberson]

Are you certain that you need to model 1 GHz for 1000 seconds?? That is what the 1000-Ts is, the upper limit on the number of seconds (not the number of samples.)

[vk]

The fix to replace 1000 with smaller number helped. Thanks