Compare and contrast continuous-time and discrete-time signals, providing definitions, mathematical examples, and sketches.

Here are the detailed answers to the questions in the picture.

1a)

• Continuous-time vs discrete-time signals:
  • Definition: A continuous-time signal $x(t)$ is defined for all real values of time $t$. A discrete-time signal $x[n]$ is defined only for integer values of time $n$.
  • Mathematical Example:
    • Continuous-time: $x(t) = \sin(2\pi t)$
    • Discrete-time: $x[n] = \cos(\pi n/4)$
  • Sketch:
    • Continuous-time: A smooth, unbroken curve.
    • Discrete-time: