Digital signal processing in the context of "Discrete cosine transform"

Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions (perhaps more), digital image processing may be modeled in the form of multidimensional systems. The generation and development of digital image processing are mainly affected by three factors: first, the development of computers; second, the development of mathematics (especially the creation and improvement of discrete mathematics theory); and third, the demand for a wide range of applications in environment, agriculture, military, industry and medical science has increased.

Cryptography, or cryptology (from Ancient Greek: κρυπτός, romanized: kryptós "hidden, secret"; and γράφειν graphein, "to write", or -λογία -logia, "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security (data confidentiality, data integrity, authentication and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords and military communications.

Cryptography prior to the modern age was effectively synonymous with encryption, converting readable information (plaintext) to unintelligible nonsense text (ciphertext), which can only be read by reversing the process (decryption). The sender of an encrypted (coded) message shares the decryption (decoding) technique only with the intended recipients to preclude access from adversaries. The cryptography literature often uses the names "Alice" (or "A") for the sender, "Bob" (or "B") for the intended recipient, and "Eve" (or "E") for the eavesdropping adversary. Since the development of rotor cipher machines in World War I and the advent of computers in World War II, cryptography methods have become increasingly complex and their applications more varied.

Musique concrète (French pronunciation: [myzik kɔ̃kʁɛt]; lit. 'concrete music') is a type of music composition that utilizes recorded sounds as raw material. Sounds are often modified through the application of audio signal processing and tape music techniques, and may be assembled into a form of sound collage. It can feature sounds derived from recordings of musical instruments, the human voice, and the natural environment, as well as those created using sound synthesis and computer-based digital signal processing. Compositions in this idiom are not restricted to the normal musical rules of melody, harmony, rhythm, and metre. The technique exploits acousmatic sound, such that sound identities can often be intentionally obscured or appear unconnected to their source cause.

The theoretical basis of musique concrète as a compositional practice was developed by French composer Pierre Schaeffer, beginning in the early 1940s. It was largely an attempt to differentiate between music based on the abstract medium of notation and that created using so-called sound objects (French: l'objet sonore). By the early 1950s, musique concrète was contrasted with "pure" elektronische Musik as then developed in West Germany – based solely on the use of electronically produced sounds rather than recorded sounds – but the distinction has since been blurred such that the term "electronic music" covers both meanings. Schaeffer's work resulted in the establishment of France's Groupe de Recherches de Musique Concrète (GRMC), which attracted important figures including Pierre Henry, Luc Ferrari, Pierre Boulez, Karlheinz Stockhausen, Edgard Varèse, and Iannis Xenakis. From the late 1960s onward, and particularly in France, the term acousmatic music (French: musique acousmatique) was used in reference to fixed media compositions that utilized both musique concrète-based techniques and live sound spatialisation.

A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing.

Computer music is the application of computing technology in music composition, to help human composers create new music or to have computers independently create music, such as with algorithmic composition programs. It includes the theory and application of new and existing computer software technologies and basic aspects of music, such as sound synthesis, digital signal processing, sound design, sonic diffusion, acoustics, electrical engineering, and psychoacoustics. The field of computer music can trace its roots back to the origins of electronic music, and the first experiments and innovations with electronic instruments at the turn of the 20th century.

The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing. In practice, it is used to select band-limiting filters to keep aliasing below an acceptable amount when an analog signal is sampled or when sample rates are changed within a digital signal processing function.

The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.

In mathematics and digital signal processing, quantization is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms.

The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error, noise or distortion. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer.

In the context of digital signal processing (DSP), a digital signal is a discrete time, quantized amplitude signal. In other words, it is a sampled signal consisting of samples that take on values from a discrete set (a countable set that can be mapped one-to-one to a subset of integers). If that discrete set is finite, the discrete values can be represented with digital words of a finite width. Most commonly, these discrete values are represented as fixed-point words (either proportional to the waveform values or companded) or floating-point words.

The process of analog-to-digital conversion produces a digital signal. The conversion process can be thought of as occurring in two steps: