Which statement describes a continuous signal?

Which statement describes a continuous signal?

• A. It is defined for all real time and can be conceptually discontinuous but is continuous for all time values.
• B. It is defined only at discrete times.
• C. It has finite energy.
• D. It is always periodic.

Answer: (A)

Continuous-time signals are defined for every real time instant. They can have jumps or other discontinuities, but at every real time t there is a defined value. That’s what makes them continuous in the time variable, even if the function isn’t smooth. This distinguishes them from discrete-time signals, which exist only at specific time instants. Finite energy or periodicity are separate properties that don’t define whether a signal is continuous in time. For example, a step function is defined for all t, even though it jumps at t = 0, so it’s a continuous-time signal.

Continuous-time signals are defined for every real time instant. They can have jumps or other discontinuities, but at every real time t there is a defined value. That’s what makes them continuous in the time variable, even if the function isn’t smooth. This distinguishes them from discrete-time signals, which exist only at specific time instants. Finite energy or periodicity are separate properties that don’t define whether a signal is continuous in time. For example, a step function is defined for all t, even though it jumps at t = 0, so it’s a continuous-time signal.