Digital signal processing in the context of Cryptographic

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:

A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on metal–oxide–semiconductor (MOS) integrated circuit chips. They are widely used in audio signal processing, telecommunications, digital image processing, radar, sonar and speech recognition systems, and in common consumer electronic devices such as mobile phones, disk drives and high-definition television (HDTV) products.

The goal of a DSP is usually to measure, filter or compress continuous real-world analog signals. Most general-purpose microprocessors can also execute digital signal processing algorithms successfully, but may not be able to keep up with such processing continuously in real-time. Also, dedicated DSPs usually have better power efficiency, thus they are more suitable in portable devices such as mobile phones because of power consumption constraints. DSPs often use special memory architectures that are able to fetch multiple data or instructions at the same time.

Analog signal processing is a type of signal processing conducted on continuous analog signals by some analog means (as opposed to the discrete digital signal processing where the signal processing is carried out by a digital process). "Analog" indicates something that is mathematically represented as a set of continuous values. This differs from "digital" which uses a series of discrete quantities to represent signal. Analog values are typically represented as a voltage, electric current, or electric charge around components in the electronic devices. An error or noise affecting such physical quantities will result in a corresponding error in the signals represented by such physical quantities.

Examples of analog signal processing include crossover filters in loudspeakers, "bass", "treble" and "volume" controls on stereos, and "tint" controls on TVs. Common analog processing elements include capacitors, resistors and inductors (as the passive elements) and transistors or op-amps (as the active elements).

Speech processing is the study of speech signals and the processing methods of signals. The signals are usually processed in a digital representation, so speech processing can be regarded as a special case of digital signal processing, applied to speech signals. Aspects of speech processing includes the acquisition, manipulation, storage, transfer and output of speech signals. Different speech processing tasks include speech recognition, speech synthesis, speaker diarization, speech enhancement, speaker recognition, etc.

Image quality can refer to the level of accuracy with which different imaging systems capture, process, store, compress, transmit and display the signals that form an image. Another definition refers to image quality as "the weighted combination of all of the visually significant attributes of an image". The difference between the two definitions is that one focuses on the characteristics of signal processing in different imaging systems and the latter on the perceptual assessments that make an image pleasant for human viewers.

Image quality should not be mistaken with image fidelity. Image fidelity refers to the ability of a process to render a given copy in a perceptually similar way to the original (without distortion or information loss), i.e., through a digitization or conversion process from analog media to digital image.

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.

A DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input or output data are shifted by half a sample.

Nasir Ahmed (born 1940) is an American electrical engineer and computer scientist. He is Professor Emeritus of Electrical and Computer Engineering at University of New Mexico (UNM). He is best known for inventing the discrete cosine transform (DCT) in the early 1970s. The DCT is the most widely used data compression transformation, the basis for most digital media standards (image, video and audio) and commonly used in digital signal processing. He also described the discrete sine transform (DST), which is related to the DCT.

Shure Inc. is an audio products corporation headquartered in the United States. It was founded by Sidney N. Shure in Chicago, Illinois, in 1925 as a supplier of radio parts kits. The company became a manufacturer of consumer and professional audio-electronics including microphones, wireless microphone systems, phonograph cartridges, discussion systems, mixers, and digital signal processing. The company also manufactures listening products, including headphones, high-end earphones, and personal monitor systems.

In speech science and phonetics, a formant is the broad spectral maximum that results from an acoustic resonance of the human vocal tract. In acoustics, a formant is usually defined as a broad peak, or local maximum, in the spectrum. For harmonic sounds, with this definition, the formant frequency is sometimes taken as that of the harmonic that is most augmented by a resonance. The difference between these two definitions resides in whether "formants" characterise the production mechanisms of a sound or the produced sound itself. In practice, the frequency of a spectral peak differs slightly from the associated resonance frequency, except when, by luck, harmonics are aligned with the resonance frequency, or when the sound source is mostly non-harmonic, as in whispering and vocal fry.

A room can be said to have formants characteristic of that particular room, due to its resonances, i.e., to the way sound reflects from its walls and objects. Room formants of this nature reinforce themselves by emphasizing specific frequencies and absorbing others, as exploited, for example, by Alvin Lucier in his piece I Am Sitting in a Room. In acoustic digital signal processing, the way a collection of formants (such as a room) affects a signal can be represented by an impulse response.

A subwoofer (or sub) is a loudspeaker designed to reproduce low-pitched audio frequencies, known as bass and sub-bass, that are lower in frequency than those which can be (optimally) generated by a woofer. The typical frequency range that is covered by a subwoofer is about 20–200 Hz for consumer products, below 100 Hz for professional live sound, and below 80 Hz in THX-certified systems. Thus, one or more subwoofers are important for high-quality sound reproduction as they are responsible for the lowest two to three octaves of the ten octaves that are audible. This very low-frequency (VLF) range reproduces the natural fundamental tones of the bass drum, electric bass, double bass, grand piano, contrabassoon, tuba, in addition to thunder, gunshots, explosions, etc.

Subwoofers are never used alone, as they are intended to substitute the VLF sounds of "main" loudspeakers that cover the higher frequency bands. VLF and higher-frequency signals are sent separately to the subwoofer(s) and the mains by a "crossover" network, typically using active electronics, including digital signal processing (DSP). Additionally, subwoofers are fed their own low-frequency effects (LFE) signals that are reproduced at 10 dB higher than standard peak level.