Digital signal (signal processing) in the context of Injective function

Videotape is magnetic tape used for storing video and usually sound in addition. Information stored can be in the form of either an analog or digital signal. The tape can come in stand-alone tape reel or inside a casing such as a tape cartridge or cassette. Videotape is used in both video tape recorders (VTRs) and, more commonly, videocassette recorders (VCRs) and camcorders. Videotapes have also been used for storing scientific or medical data, such as the data produced by an electrocardiogram.

Because video signals have a very high bandwidth, and stationary heads would require extremely high tape speeds, in most cases, a helical-scan video head rotates against the moving tape to record the data in two dimensions.

An audio signal is a representation of sound, typically using either a changing level of electrical voltage for analog signals or a series of binary numbers for digital signals. Audio signals have frequencies in the audio frequency range of roughly 20 to 20,000 Hz, which corresponds to the lower and upper limits of human hearing. Audio signals may be synthesized directly, or may originate at a transducer such as a microphone, musical instrument pickup, phonograph cartridge, or tape head. Loudspeakers or headphones convert an electrical audio signal back into sound.

Digital audio systems represent audio signals in a variety of digital formats.

Digital audio is a representation of sound recorded in, or converted into, digital form. In digital audio, the sound wave of the audio signal is typically encoded as numerical samples in a continuous sequence. For example, in CD audio, samples are taken 44,100 times per second, each with 16-bit resolution. Digital audio is also the name for the entire technology of sound recording and reproduction using audio signals that have been encoded in digital form. Following significant advances in digital audio technology during the 1970s and 1980s, it gradually replaced analog audio technology in many areas of audio engineering, record production and telecommunications in the 1990s and 2000s.

In a digital audio system, an analog electrical signal representing the sound is converted with an analog-to-digital converter (ADC) into a digital signal, typically using pulse-code modulation (PCM). This digital signal can then be recorded, edited, modified, and copied using computers, audio playback machines, and other digital tools. For playback, a digital-to-analog converter (DAC) performs the reverse process, converting a digital signal back into an analog signal, which is then sent through an audio power amplifier and ultimately to a loudspeaker.

Audio signal processing is a subfield of signal processing that is concerned with the electronic manipulation of audio signals. Audio signals are electronic representations of sound waves—longitudinal waves which travel through air, consisting of compressions and rarefactions. The energy contained in audio signals or sound power level is typically measured in decibels. As audio signals may be represented in either digital or analog format, processing may occur in either domain. Analog processors operate directly on the electrical signal, while digital processors operate mathematically on its digital representation.

In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as from fingers touching a touchscreen, sound entering a microphone, or light entering a digital camera, into a digital signal.

An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.

In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.

DACs are commonly used in music players to convert digital data streams into analog audio signals. They are also used in televisions and mobile phones to convert digital video data into analog video signals. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type, while the video DAC is a high-frequency low- to medium-resolution type.

A mixing console or mixing desk is an electronic device for mixing audio signals, used in sound recording and reproduction and sound reinforcement systems. Inputs to the console include microphones, signals from electric or electronic instruments, or recorded sounds. Mixers may control analog or digital signals. The modified signals are summed to produce the combined output signals, which can then be broadcast, amplified through a sound reinforcement system or recorded.

Mixing consoles are used for applications including recording studios, public address systems, sound reinforcement systems, nightclubs, broadcasting, and post-production. A typical, simple application combines signals from microphones on stage into an amplifier that drives one set of loudspeakers for the audience. A DJ mixer may have only two channels, for mixing two record players. A coffeehouse's small stage might only have a six-channel mixer, enough for two singer-guitarists and a percussionist. A nightclub stage's mixer for rock music shows may have 24 channels for mixing the signals from a rhythm section, lead guitar and several vocalists. A mixing console in a professional recording studio may have as many as 96 channels. Consoles used for live sound can go even higher, with some having up to 384 input channels.

Audiotape is magnetic tape used for storing audio. Information stored can be in the form of either an analog or digital signal. Audiotape can be used in various tape recorders including machines for reel-to-reel audio tape recording on open reels or they can be enclosed in cases that only have one reel (tape cartridge) or two reels (cassette).

Sound can be recorded and stored and played using either digital or analog techniques. Both techniques introduce errors and distortions in the sound, and these methods can be systematically compared. Musicians and listeners have argued over the superiority of digital versus analog sound recordings. Arguments for analog systems include the absence of fundamental error mechanisms which are present in digital audio systems, including aliasing and associated anti-aliasing filter implementation, jitter and quantization noise. Advocates of digital point to the high levels of performance possible with digital audio, including excellent linearity in the audible band and low levels of noise and distortion.

Two prominent differences in performance between the two methods are the bandwidth and the signal-to-noise ratio (S/N ratio). The bandwidth of the digital system is determined, according to the Nyquist frequency, by the sample rate used. The bandwidth of an analog system is dependent on the physical and electronic capabilities of the analog circuits. The S/N ratio of a digital system may be limited by the bit depth of the digitization process, but the electronic implementation of conversion circuits introduces additional noise. In an analog system, other natural analog noise sources exist, such as flicker noise and imperfections in the recording medium. Other performance differences are specific to the systems under comparison, such as the ability for more transparent filtering algorithms in digital systems and the harmonic saturation and speed variations of analog systems.

Pulse-code modulation (PCM) is a method used to digitally represent analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the amplitude of the analog signal is sampled at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps. Shannon, Oliver, and Pierce were inducted into the National Inventors Hall of Fame for their PCM patent granted in 1952.

Linear pulse-code modulation (LPCM) is a specific type of PCM in which the quantization levels are linearly uniform. This is in contrast to PCM encodings in which quantization levels vary as a function of amplitude (as with the A-law algorithm or the μ-law algorithm). Though PCM is a more general term, it is often used to describe data encoded as LPCM.

High dynamic range (HDR), also known as wide dynamic range, extended dynamic range, or expanded dynamic range, is a signal with a higher dynamic range than usual.

The term is often used in discussing the dynamic ranges of images, videos, audio or radio. It may also apply to the means of recording, processing, and reproducing such signals including analog and digitized signals.