Signals and Their Characteristics

Signals and Their Characteristics

• A signal is a function representing a physical quantity or variable and typically contains information about the behavior of a phenomenon.

Continuous-Time (CT) and Discrete-Time (DT) Signals

• A signal is continuous-time if it is a continuous variable.
• A signal is discrete-time if it is defined at discrete times.
• A continuous-time signal can take on any value in a continuous interval, making it an analog signal.
• A discrete-time signal can take on only a finite number of distinct values, making it a digital signal.

Real and Complex Signals

• Signals can be real or complex.
• A general complex signal x(t) is a function of the form x(t) = s(t) + jv(t), where s(t) and v(t) are real signals.

Deterministic and Random Signals

• Deterministic signals are those signals whose values are completely specified.
• Random signals take on random values at any given time.

Even and Odd Signals

• Even signals: x(-t) = x(t) or x[-n] = x[n].
• Odd signals: x(-t) = -x(t) or x[-n] = -x[n].
• Any signal can be expressed as the sum of an even signal and an odd signal.

Periodic and Non-Periodic Signals

• A CT signal x(t) is said to be periodic with period ‘T’ if x(t + T) = x(t) for all t.
• A DT signal x[n] is periodic with period N if x[n + N] = x[n].
• Any DT or CT signal which is not periodic is non-periodic or aperiodic.

Basic Continuous-Time Signals

• The CT complex exponential signal is of the form x(t) = Ce^(at).
• If C and a are real, then x(t) is a real exponential of the form x(t) = C*e^(at).
• If a > 0, then the signal is linearly compressed.

Time-Shifting and Time-Scaling Operations

• The time-shifting operation is performed first on x(t) resulting in an intermediate signal.
• Then, time scaling (or reversal) is performed on the intermediate signal resulting in the desired output.