Licchavi Lyceum


Licchavi Lyceum

Continuous & Discrete Time Signal

Continuous Time Signal are mathematical representations of signals that vary continuously over time. They are defined and observed at every instant of time within a specified interval. In other words, a continuous-time signal is defined for an infinite number of points in time. Continuous & Discrete Time Signal:

Continuous & Discrete Time Signal
Continuous & Discrete Time Signal

A continuous-time signal can take on various forms and can represent a wide range of physical quantities or phenomena. Some examples of continuous-time signals include:

  1. Analog audio signals: Continuous-time signals are used to represent sounds in the form of electrical voltage variations. For example, the waveform produced by a microphone capturing someone’s voice or a musical instrument is a continuous-time signal.
  2. Voltage waveforms: In electrical engineering, voltage signals that vary continuously over time are represented as continuous-time signals. These can include periodic waveforms like sine waves, square waves, and triangular waves, as well as non-periodic signals.
  3. Temperature measurements: Temperature variations over time, such as the temperature of a room or the temperature of a chemical process, can be represented as continuous-time signals.
  4. Biomedical signals: Signals related to physiological processes, such as electrocardiogram (ECG) and electroencephalogram (EEG), are continuous-time signals that represent the electrical activity of the heart and brain, respectively.
  5. Sensor measurements: Signals obtained from various sensors, such as pressure sensors, humidity sensors, and motion sensors, can be represented as continuous-time signals.

Mathematically, continuous-time signals are typically represented by functions of time, denoted as x(t), where t represents the continuous time variable. These signals can be further analyzed, processed, and manipulated using various techniques and tools in continuous-time signal processing, such as Fourier analysis, filtering, modulation, and system modeling.

It’s important to note that continuous-time signals are often converted into discrete-time signals for digital processing and analysis using techniques such as sampling, where the continuous-time signal is sampled at discrete intervals to obtain a discrete representation of the original signal.

Sine Wave Plot

Sine Wave Plot

Discrete time Signal

Discrete time signal is defined at specific points or intervals in time. These signals are typically represented as sequences of values. Examples of discrete-time signals include digital audio signals, sampled temperature measurements, and binary sequences.

Discrete-time systems are mathematical models that operate on discrete-time signals. They can be represented by difference equations or difference equations in the z-domain. These systems take discrete-time signals as input and produce discrete-time signals as output. Examples of discrete-time systems include digital filters, digital controllers, and digital communication systems.

Representation of Continuous-Time Signals and Systems

Continuous-time signals can be represented using mathematical functions, such as:

  • Time-domain representation: x(t), where t represents the continuous time variable.
  • Frequency-domain representation: X(f), where f represents the continuous frequency variable.

Continuous-time systems can be represented by differential equations or transfer functions, such as:

  • Differential equation representation: dx(t)/dt + a1x(t) + a0x(t) = b0u(t), where dx(t)/dt represents the derivative of x(t) with respect to time, and u(t) represents the input.
  • Transfer function representation: H(s), where s represents the complex frequency variable.

Discrete-time signals can be represented using sequences of values, such as:

  • Time-domain representation: x[n], where n represents the discrete time index.
  • Frequency-domain representation: X[k], where k represents the discrete frequency index.

Discrete-time systems can be represented by different equations or transfer functions in the z-domain, such as:

  • Difference equation representation: y[n] = a1y[n-1] + a0y[n-2] + b0u[n], where y[n] represents the output, u[n] represents the input, and a0, a1, and b0 are coefficients.
  • Transfer function representation: H(z), where z represents the complex variable in the z-domain.

It’s important to note that these representations are just a few examples, and there are various other mathematical representations and transformations used to analyze and design continuous-time and discrete-time signals and systems.

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