ChirpA chirp is a signal in which the frequency increases (up-chirp) or decreases (down-chirp) with time. In some sources, the term chirp is used interchangeably with sweep signal. It is commonly applied to sonar, radar, and laser systems, and to other applications, such as in spread-spectrum communications (see chirp spread spectrum). This signal type is biologically inspired and occurs as a phenomenon due to dispersion (a non-linear dependence between frequency and the propagation speed of the wave components).
Sparse dictionary learningSparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims at finding a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. These elements are called atoms and they compose a dictionary. Atoms in the dictionary are not required to be orthogonal, and they may be an over-complete spanning set. This problem setup also allows the dimensionality of the signals being represented to be higher than the one of the signals being observed.
Very Large TelescopeThe Very Large Telescope (VLT) is a facility operated by the European Southern Observatory, located on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each equipped with a primary mirror that measures 8.2 meters in diameter. These optical telescopes, named Antu, Kueyen, Melipal, and Yepun (all words for astronomical objects in the Mapuche language), are generally used separately but can be combined to achieve a very high angular resolution.
Aperture synthesisAperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection. At each separation and orientation, the lobe-pattern of the interferometer produces an output which is one component of the Fourier transform of the spatial distribution of the brightness of the observed object. The image (or "map") of the source is produced from these measurements.
Sparse approximationSparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in , signal processing, machine learning, medical imaging, and more. Consider a linear system of equations , where is an underdetermined matrix and . The matrix (typically assumed to be full-rank) is referred to as the dictionary, and is a signal of interest.
Matching pursuitMatching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary . The basic idea is to approximately represent a signal from Hilbert space as a weighted sum of finitely many functions (called atoms) taken from . An approximation with atoms has the form where is the th column of the matrix and is the scalar weighting factor (amplitude) for the atom . Normally, not every atom in will be used in this sum.
Continuous waveA continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particle accelerator having a continuous output, as opposed to a pulsed output. By extension, the term continuous wave also refers to an early method of radio transmission in which a sinusoidal carrier wave is switched on and off. This is more precisely called interrupted continuous wave (ICW).
Spread spectrumIn telecommunication, especially radio communication, spread spectrum designates techniques by which a signal (e.g., an electrical, electromagnetic, or acoustic) generated with a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth. Spread-spectrum techniques are used for the establishment of secure communications, increasing resistance to natural interference, noise, and jamming, to prevent detection, to limit power flux density (e.g.
Unit of measurementA unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity. The metre (symbol m) is a unit of length that represents a definite predetermined length. For instance, when referencing "10 metres" (or 10 m), what is actually meant is 10 times the definite predetermined length called "metre".
Compressed sensingCompressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. There are two conditions under which recovery is possible.
