Confusion regarding "step value" of time in discrete time signals?

Question

I am reading book"Signals and Systems Laboratory with Matlab" and i am studying about discrete time signals

I have also attached a snap and highlighted a line:

The definition of the time. For discrete-time signals, time is defined by using step 1

Does that means when we define a discrete time signal in MATLAB ,its increment/step should be "1"? Well that is the default case in MATLAB that if we define a time vector t=[0:5]; we will have values 0,1,2,3,4 and 5 and step/spacing between values will be "1"

So does that means that we can't have any value other than "1" as spacing/step??

Answer 1

Using a step of one normalizes time to be in units of samples, which is commonly done in time for discrete-time signal processing. (Or if in units of seconds, the step is in 1 second increments).

This is also done for frequency, with the equivalent normalized units of frequency as cycles/sample instead of Hz or radians/sample instead of radians/sec. Both are achieved by dividing the frequency in Hz or rad/sec by the sampling rate (thus normalized). Thus the frequency axis when extending from DC to the sampling rate would extend from $0$ to $1$ in units of cycles/sample or from $0$ to $2\pi$ in units of radians/sample. Similarly if you multiply time by the sampling rate, you convert time in units of seconds to units of samples.

This is convenient but if it is desired to observe processes in units of seconds, you can just as well use the actual time step in seconds as the increment.