17.1 Signal classification and representation

Signals come in various flavors: continuous or discrete, analog or digital. They can be periodic, repeating at regular intervals, or aperiodic. Understanding these types helps us grasp how signals behave in different systems.

Signals can also be classified based on predictability. Deterministic signals follow a specific rule, while random signals are unpredictable. We can represent signals in time or frequency domains, each offering unique insights into signal behavior.

Signal Types

Continuous and Discrete Signals

Top images from around the web for Continuous and Discrete Signals

• 

  The difference between convolution and cross-correlation from a signal-analysis point of view ... View original

  Is this image relevant?

• 

  Discrete-time Fourier transform - Wikipedia View original

  Is this image relevant?

• 

  Difference between Digital signal and Discrete signal - Signal Processing Stack Exchange View original

  Is this image relevant?

• 

  The difference between convolution and cross-correlation from a signal-analysis point of view ... View original

  Is this image relevant?

• 

  Discrete-time Fourier transform - Wikipedia View original

  Is this image relevant?

1 of 3

Top images from around the web for Continuous and Discrete Signals

• 

  The difference between convolution and cross-correlation from a signal-analysis point of view ... View original

  Is this image relevant?

• 

  Discrete-time Fourier transform - Wikipedia View original

  Is this image relevant?

• 

  Difference between Digital signal and Discrete signal - Signal Processing Stack Exchange View original

  Is this image relevant?

• 

  The difference between convolution and cross-correlation from a signal-analysis point of view ... View original

  Is this image relevant?

• 

  Discrete-time Fourier transform - Wikipedia View original

  Is this image relevant?

1 of 3

• Continuous-time signals defined for all values of time $t$ and take on a continuum of values
• Discrete-time signals defined only at discrete time instants (typically represented as a sequence of numbers)
• Continuous-time signals often result from natural phenomena (temperature, pressure, sound waves)
• Discrete-time signals often result from sampling continuous-time signals at regular intervals ($T_s$)

Analog and Digital Signals

• Analog signals can take on any value within a continuous range of values
• Digital signals can only take on a finite number of distinct values (often represented by binary digits or bits)
• Analog signals are typically continuous-time signals (voltage, current, temperature)
• Digital signals are typically discrete-time signals (digital audio, digital images)
• Analog-to-digital conversion (ADC) converts analog signals to digital signals by sampling and quantization

Signal Periodicity

Periodic Signals

• Periodic signals repeat themselves at regular intervals (period $T$)
• Mathematically, a signal $x(t)$ is periodic if $x(t) = x(t + T)$ for all values of $t$
• Examples of periodic signals include sinusoidal waves, square waves, and sawtooth waves
• Periodic signals have a fundamental frequency ($f_0 = 1/T$) and harmonics (integer multiples of $f_0$)

Aperiodic Signals

• Aperiodic signals do not exhibit a regular repetition pattern
• Aperiodic signals can be further classified as almost periodic or non-periodic
• Almost periodic signals consist of multiple periodic components with periods that are not integer multiples of each other
• Non-periodic signals do not have any repeating patterns (random noise, transient signals)

Signal Predictability

Deterministic Signals

• Deterministic signals can be described by a mathematical function or rule
• The value of a deterministic signal at any given time can be predicted with certainty
• Examples of deterministic signals include sinusoidal waves, exponential functions, and polynomial functions
• Deterministic signals can be further classified as periodic or aperiodic

Random Signals

• Random signals cannot be described by a specific mathematical function
• The value of a random signal at any given time cannot be predicted with certainty
• Random signals are characterized by their statistical properties (mean, variance, probability density function)
• Examples of random signals include thermal noise, shot noise, and random walk processes
• Random signals can be stationary (statistical properties do not change over time) or non-stationary

Signal Representation

Time-Domain Representation

• Time-domain representation describes a signal as a function of time $x(t)$
• Provides information about the signal's amplitude and how it changes over time
• Useful for analyzing transient behavior, time-localized events, and system response to inputs
• Examples of time-domain analysis include plotting signal waveforms and calculating signal energy

Frequency-Domain Representation

• Frequency-domain representation describes a signal as a function of frequency $X(f)$
• Obtained by applying the Fourier transform to the time-domain representation
• Provides information about the signal's frequency content and the relative importance of different frequencies
• Useful for analyzing periodic signals, bandwidth, and frequency response of systems
• Examples of frequency-domain analysis include plotting frequency spectra and calculating signal bandwidth