13.2:
Classification of Signals
Signals are categorized as Continuous-time or discrete-time, Periodic or aperiodic, Analog or digital, and Causal or noncausal.
A continuous-time signal holds value at every moment, while a discrete-time signal holds value only at specific moments.
Discrete-time signals, often denoted by x of n, where n is an integer, usually represent phenomena with inherently discrete variables.
A continuous-time periodic signal, such as a sinusoid, repeats itself every T seconds, adhering to the periodicity condition. Any signal that does not satisfy the periodicity condition is called an aperiodic signal.
A discrete-time periodic signal, with a period of positive integer N, remains unaltered after a time shift of N. A discrete-time periodic signal can be represented as a sum of complex exponentials, particularly when analyzed using Fourier series.
An analog signal is a continuous-time signal with amplitude values that can vary continuously within a given range. A digital signal is a discrete-time signal with amplitude values restricted to a finite set of possible levels.
A signal is considered causal if it is zero for all negative time values. A signal that exists for negative time values is called noncausal.
13.2:
Classification of Signals
In signal processing, signals are classified based on various characteristics: continuous-time versus discrete-time, periodic versus aperiodic, analog versus digital, and causal versus noncausal. Each category highlights distinct properties crucial for understanding and manipulating signals.
A continuous-time signal holds a value at every instant in time, representing information seamlessly. In contrast, a discrete-time signal holds values only at specific moments, often denoted as x(n), where n is an integer. Discrete-time signals typically arise from phenomena with inherently discrete variables, such as digital audio samples.
Periodic signals repeat patterns over time. A continuous-time periodic signal, like a sinusoidal wave, repeats every t seconds, satisfying the periodicity condition.
Signals not meeting this condition are termed aperiodic. For discrete-time signals, periodicity implies the signal remains unchanged after a time shift of n periods, as described by,
These signals can also be represented in complex exponential form, crucial for many applications.
Analog and digital signals are differentiated based on amplitude. An analog signal, continuous in time, can assume any value within a range, providing a smooth data representation. A digital signal, a type of discrete-time signal, can adopt values only from a finite set, making it suitable for digital systems and computation.
The causality of a signal is determined by its existence over time. A continuous-time signal is causal if it is zero for all negative time instances, indicating the signal does not anticipate future values. Conversely, a noncausal signal holds values for negative times, implying it relies on future input values. Understanding these classifications is essential for effective signal analysis and processing in fields like telecommunications, control systems, and digital signal processing.