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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 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.
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse factors. As a result, it manages to reduce the complexity of computing the DFT from , which arises if one simply applies the definition of DFT, to , where is the data size. The difference in speed can be enormous, especially for long data sets where N may be in the thousands or millions. In the presence of round-off error, many FFT algorithms are much more accurate than evaluating the DFT definition directly or indirectly. There are many different FFT algorithms based on a wide range of published theories, from simple complex-number arithmetic to group theory and number theory.
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, images, potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality, and to also detect or pinpoint components of interest in a measured signal.
In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates trellis decoding using a time-invariant trellis. Time invariant trellis decoding allows convolutional codes to be maximum-likelihood soft-decision decoded with reasonable complexity.
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 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 ; third, the demand for a wide range of applications in environment, agriculture, military, industry and medical science has increased.
Télécom Paris is a French public institution for higher education and engineering research. Located in Palaiseau, it is also a member of the Institut Polytechnique de Paris and the Institut Mines-Télécom. In 2021 it was the sixth highest ranked French university in the World University Rankings, and the 7th best small university worldwide. In the QS Ranking, Télécom Paris is the 64th best university worldwide in Computer Science.
Andrew James Viterbi is an Italian Jewish–American electrical engineer and businessman who co-founded Qualcomm Inc. and invented the Viterbi algorithm. He is the Presidential Chair Professor of Electrical Engineering at the University of Southern California's Viterbi School of Engineering, which was named in his honor in 2004 in recognition of his $52 million gift.
In computer data storage, partial-response maximum-likelihood (PRML) is a method for recovering the digital data from the weak analog read-back signal picked up by the head of a magnetic disk drive or tape drive. PRML was introduced to recover data more reliably or at a greater areal-density than earlier simpler schemes such as peak-detection. These advances are important because most of the digital data in the world is stored using magnetic storage on hard disk or tape drives.
David John Wheeler FRS was a computer scientist and professor of computer science at the University of Cambridge.
Lawrence R. Rabiner is an electrical engineer working in the fields of digital signal processing and speech processing; in particular in digital signal processing for automatic speech recognition. He has worked on systems for AT&T Corporation for speech recognition.
Shmuel Winograd was an Israeli-American computer scientist, noted for his contributions to computational complexity. He has proved several major results regarding the computational aspects of arithmetic; his contributions include the Coppersmith–Winograd algorithm and an algorithm for the fast Fourier transform which transforms it into a problem of computing convolutions which can be solved with another Winograd's algorithm.
László "Les" Bélády was a Hungarian computer scientist notable for devising the Bélády's Min theoretical memory caching algorithm in 1966 while working at IBM Research. He also demonstrated the existence of a Bélády's anomaly. During the 1980s, he was the editor-in-chief of the IEEE Transactions on Software Engineering.
Richard Blahut, former chair of the Electrical and Computer Engineering Department at the University of Illinois at Urbana–Champaign, is best known for his work in information theory. He received his PhD Electrical Engineering from Cornell University in 1972.
Martin Vetterli is the current president of École polytechnique fédérale de Lausanne (EPFL) in Switzerland, succeeding Patrick Aebischer. He's a professor of engineering and was formerly the president of the National Research Council of the Swiss National Science Foundation.
Yann André LeCun is a Turing Award winning French computer scientist working primarily in the fields of machine learning, computer vision, mobile robotics and computational neuroscience. He is the Silver Professor of the Courant Institute of Mathematical Sciences at New York University and Vice-President, Chief AI Scientist at Meta.
Block-matching and 3D filtering (BM3D) is a 3-D block-matching algorithm used primarily for noise reduction in images. It is one of the expansions of the non-local means methodology. There are two cascades in BM3D: a hard-thresholding and a Wiener filter stage, both involving the following parts: grouping, collaborative filtering, and aggregation. This algorithm depends on an augmented representation in the transformation site.
Boi Volkert Faltings is a Swiss professor of artificial intelligence at École Polytechnique Fédérale de Lausanne.
Patrick Flandrin is a French physicist, research director at CNRS researcher at École Normale Supérieure de Lyon, and member of the French Academy of Sciences.
Éric Moulines is a French researcher in statistical learning and signal processing. He received the silver medal from the CNRS in 2010, the France Télécom prize awarded in collaboration with the French Academy of Sciences in 2011. He was appointed a Fellow of the European Association for Signal Processing in 2012 and of the Institute of Mathematical Statistics in 2016. He is General Engineer of the Corps des Mines (X81).
