Multidimensional transformIn mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions. One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation to a frequency domain representation. The discrete-domain multidimensional Fourier transform (FT) can be computed as follows: where F stands for the multidimensional Fourier transform, m stands for multidimensional dimension.
Speech processingSpeech 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.
Discrete two-point spaceIn topology, a branch of mathematics, a discrete two-point space is the simplest example of a totally disconnected discrete space. The points can be denoted by the symbols 0 and 1. Any disconnected space has a continuous mapping which is not constant onto the discrete two-point space. Conversely if a nonconstant continuous mapping to the discrete two-point space exists from a topological space, the space is disconnected.
Generalized Fourier seriesIn mathematical analysis, many generalizations of Fourier series have proved to be useful. They are all special cases of decompositions over an orthonormal basis of an inner product space. Here we consider that of square-integrable functions defined on an interval of the real line, which is important, among others, for interpolation theory. Consider a set of square-integrable functions with values in or , which are pairwise orthogonal for the inner product where is a weight function, and represents complex conjugation, i.
Sampling designIn the theory of finite population sampling, a sampling design specifies for every possible sample its probability of being drawn. Mathematically, a sampling design is denoted by the function which gives the probability of drawing a sample During Bernoulli sampling, is given by where for each element is the probability of being included in the sample and is the total number of elements in the sample and is the total number of elements in the population (before sampling commenced).
MicrophonicsMicrophonics, microphony, or microphonism describes the phenomenon wherein certain components in electronic devices transform mechanical vibrations into an undesired electrical signal (noise). The term comes from analogy with a microphone, which is intentionally designed to convert vibrations to electrical signals. When electronic equipment was built using vacuum tubes, microphonics were often a serious design problem.
Christiaan HuygensChristiaan Huygens, Lord of Zeelhem, (ˈhaɪɡənz , USˈhɔɪɡənz , ˈkrɪstijaːn ˈɦœyɣə(n)s; also spelled Huyghens; Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan.
