Discrete-time signals are Continuous in amplitude and discrete in time

Definition of Discrete-time Signals:
A discrete-time signal is a sequence of values that is defined only at specific points in time. The values of a discrete-time signal are usually represented as amplitudes at equally spaced time intervals. These time intervals are discrete and separated by a fixed duration.

Explanation:
To understand why discrete-time signals are continuous in amplitude and discrete in time, let's break down the characteristics of these signals.

Continuous in amplitude:
- Amplitude refers to the magnitude or intensity of the signal.
- In discrete-time signals, the amplitude is continuous, meaning it can take on any value within a certain range.
- For example, if we have a discrete-time signal representing the temperature of a room, the amplitude can be any real number within the range of possible temperatures.

Discrete in time:
- Time refers to the instances or points at which the signal is defined.
- In discrete-time signals, the time is discrete, meaning it is defined only at specific points or intervals.
- These intervals are equally spaced and separated by a fixed duration.
- For example, if we have a discrete-time signal representing the voltage of an electrical circuit, the time instances could be measured every second, and the signal would be defined only at those specific time points.

Illustration:
Let's consider an example to further illustrate this concept. Suppose we have a discrete-time signal representing the daily temperature readings at noon for a week. The signal values would be the temperatures recorded at noon each day, and the time instances would be the days of the week.

- The amplitude of the signal would represent the temperature values, which can take on any real number within the range of possible temperatures.
- The time instances would be discrete and separated by a fixed duration of one day.

Conclusion:
In summary, discrete-time signals are continuous in amplitude because they can take on any value within a certain range. However, they are discrete in time because they are defined only at specific points or intervals, which are equally spaced and separated by a fixed duration.