Digital signal (signal processing)

A digital signal in signal processing is a discrete-time signal whose amplitude is discrete, taking on only a finite number of values. Unlike analog signals, which are continuous in both time and amplitude, digital signals are represented by a sequence of discrete values, typically binary (0 or 1). These discrete values are often referred to as "bits" or "samples."

Digital signals are commonly created by converting analog signals using a process called analog-to-digital conversion (ADC). This process involves sampling the analog signal at regular intervals and then quantizing the amplitude of each sample to one of the predefined discrete levels. The resolution of the quantization (the number of discrete levels) determines the accuracy of the digital representation. A higher resolution (more levels) leads to a more accurate representation of the original analog signal, but also requires more storage space.

Key characteristics of digital signals include:

• Discrete-time: The signal is defined only at specific points in time, not continuously. These points are determined by the sampling rate.
• Discrete-amplitude: The signal's amplitude can only take on a finite number of distinct values.
• Quantization: The process of mapping the continuous amplitude of an analog signal to a finite set of discrete levels. Quantization introduces quantization error, which is the difference between the original analog value and its digital approximation.
• Sampling rate: The number of samples taken per unit of time. According to the Nyquist-Shannon sampling theorem, the sampling rate must be at least twice the highest frequency component of the analog signal being converted to avoid aliasing.
• Bit depth: The number of bits used to represent each sample. A higher bit depth allows for a finer quantization and therefore a more accurate representation of the analog signal.

Digital signals are widely used in modern electronics and communication systems due to their robustness to noise, ease of storage, manipulation, and processing using digital circuits and computers. They are also more amenable to error detection and correction than analog signals. Common applications include digital audio, digital video, digital communication, and control systems. The ability to perform complex mathematical operations on digital signals via digital signal processing (DSP) techniques is a significant advantage over analog signal processing.