Which statement correctly characterizes discrete-time signals?

• A. They are defined only at specific points in time
• B. They are defined at every instant in time
• C. They have continuous-valued amplitudes
• D. They cannot be processed digitally

Answer: (A)

Discrete-time signals are defined only at specific time samples, forming a sequence indexed by integers. In practice, you obtain them by sampling a continuous signal at regular intervals, so you get values x[n] only at n = 0, 1, 2, … and nothing is defined between those instants. This is what makes them discrete in time.

The amplitude of a discrete-time signal can be any real (or even discrete) value, so having continuous-valued amplitudes is not a defining requirement. A discrete-time signal need not have amplitudes restricted to integers, for example.

If a signal were defined at every instant in time, that would be a continuous-time signal, not a discrete-time one. And digital processing is precisely what discrete-time signals are designed for—they are the type of data digital systems manipulate, store, and analyze.

So the statement that they are defined only at specific points in time best captures their essential nature.