en.unionpedia.org

Generalized pencil-of-function method, the Glossary

Generalized pencil-of-function method (GPOF), also known as matrix pencil method, is a signal processing technique for estimating a signal or extracting information with complex exponentials.^[1]

45 relations: Angular frequency, Antenna (radio), Band-pass filter, Complex number, Computational electromagnetics, Conjugate transpose, Cramér–Rao bound, Damping, Diagonal matrix, Digital filter, Eigendecomposition of a matrix, Eigenvalues and eigenvectors, Electrical engineering, Estimation of signal parameters via rotational invariance techniques, Exponential function, Finite impulse response, Green's function, IEEE Transactions on Antennas and Propagation, IEEE Transactions on Microwave Theory and Techniques, IEEE Transactions on Signal Processing, Infinite impulse response, Least squares, Matrix pencil, Method of moments (electromagnetics), Microwave engineering, Monolithic microwave integrated circuit, Moore–Penrose inverse, Moving target indication, MUSIC (algorithm), Noise (signal processing), Prony's method, Radar signal characteristics, Residue (complex analysis), Sampling (signal processing), Scattering parameters, Series acceleration, Signal processing, Signal-to-noise ratio, Significant figures, Singular value, Singular value decomposition, Tapan Sarkar, Unitary matrix, Z-transform, Zeros and poles.
Computational electromagnetics
Radar signal processing
Signal estimation

Angular frequency

In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves).

See Generalized pencil-of-function method and Angular frequency

Antenna (radio)

In radio engineering, an antenna (American English) or aerial (British English) is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver.

See Generalized pencil-of-function method and Antenna (radio)

Band-pass filter

A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.

See Generalized pencil-of-function method and Band-pass filter

Complex number

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.

See Generalized pencil-of-function method and Complex number

Computational electromagnetics

Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment using computers.

See Generalized pencil-of-function method and Computational electromagnetics

Conjugate transpose

In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an m \times n complex matrix \mathbf is an n \times m matrix obtained by transposing \mathbf and applying complex conjugation to each entry (the complex conjugate of a+ib being a-ib, for real numbers a and b).

See Generalized pencil-of-function method and Conjugate transpose

Cramér–Rao bound

In estimation theory and statistics, the Cramér–Rao bound (CRB) relates to estimation of a deterministic (fixed, though unknown) parameter.

See Generalized pencil-of-function method and Cramér–Rao bound

Damping

In physical systems, damping is the loss of energy of an oscillating system by dissipation.

See Generalized pencil-of-function method and Damping

Diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices.

See Generalized pencil-of-function method and Diagonal matrix

Digital filter

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal.

See Generalized pencil-of-function method and Digital filter

Eigendecomposition of a matrix

In linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.

See Generalized pencil-of-function method and Eigendecomposition of a matrix

Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector is a vector that has its direction unchanged by a given linear transformation.

See Generalized pencil-of-function method and Eigenvalues and eigenvectors

Electrical engineering

Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism.

See Generalized pencil-of-function method and Electrical engineering

Estimation of signal parameters via rotational invariance techniques

Estimation of signal parameters via rotational invariant techniques (ESPRIT), is a technique to determine the parameters of a mixture of sinusoids in background noise. Generalized pencil-of-function method and Estimation of signal parameters via rotational invariance techniques are signal estimation.

See Generalized pencil-of-function method and Estimation of signal parameters via rotational invariance techniques

Exponential function

The exponential function is a mathematical function denoted by f(x).

See Generalized pencil-of-function method and Exponential function

Finite impulse response

In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time.

See Generalized pencil-of-function method and Finite impulse response

Green's function

In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.

See Generalized pencil-of-function method and Green's function

IEEE Transactions on Antennas and Propagation

IEEE Transactions on Antennas and Propagation is a peer-reviewed scientific journal published by the IEEE Antennas & Propagation Society.

See Generalized pencil-of-function method and IEEE Transactions on Antennas and Propagation

IEEE Transactions on Microwave Theory and Techniques

IEEE Transactions on Microwave Theory and Techniques (T-MTT) is a monthly peer-reviewed scientific journal with a focus on that part of engineering and theory associated with microwave/millimeter-wave technology and components, electronic devices, guided wave structures and theory, electromagnetic theory, and Radio Frequency Hybrid and Monolithic Integrated Circuits, including mixed-signal circuits, from a few MHz to THz.

See Generalized pencil-of-function method and IEEE Transactions on Microwave Theory and Techniques

IEEE Transactions on Signal Processing

The IEEE Transactions on Signal Processing is a biweekly peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers covering research on signal processing.

See Generalized pencil-of-function method and IEEE Transactions on Signal Processing

Infinite impulse response

Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response h(t) that does not become exactly zero past a certain point but continues indefinitely.

See Generalized pencil-of-function method and Infinite impulse response

Least squares

The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation.

See Generalized pencil-of-function method and Least squares

Matrix pencil

In linear algebra, if A_0, A_1,\dots,A_\ell are n\times n complex matrices for some nonnegative integer \ell, and A_\ell \ne 0 (the zero matrix), then the matrix pencil of degree \ell is the matrix-valued function defined on the complex numbers L(\lambda).

See Generalized pencil-of-function method and Matrix pencil

Method of moments (electromagnetics)

The method of moments (MoM), also known as the moment method and method of weighted residuals, is a numerical method in computational electromagnetics. Generalized pencil-of-function method and method of moments (electromagnetics) are computational electromagnetics.

See Generalized pencil-of-function method and Method of moments (electromagnetics)

Microwave engineering

Microwave engineering pertains to the study and design of microwave circuits, components, and systems.

See Generalized pencil-of-function method and Microwave engineering

Monolithic microwave integrated circuit

Monolithic microwave integrated circuit, or MMIC (sometimes pronounced "mimic"), is a type of integrated circuit (IC) device that operates at microwave frequencies (300 MHz to 300 GHz).

See Generalized pencil-of-function method and Monolithic microwave integrated circuit

Moore–Penrose inverse

In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix, often called the pseudoinverse, is the most widely known generalization of the inverse matrix.

See Generalized pencil-of-function method and Moore–Penrose inverse

Moving target indication

Moving target indication (MTI) is a mode of operation of a radar to discriminate a target against the clutter. Generalized pencil-of-function method and Moving target indication are radar signal processing.

See Generalized pencil-of-function method and Moving target indication

MUSIC (algorithm)

MUSIC (MUltiple SIgnal Classification) is an algorithm used for frequency estimation and radio direction finding.

See Generalized pencil-of-function method and MUSIC (algorithm)

Noise (signal processing)

In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion. Generalized pencil-of-function method and noise (signal processing) are signal processing.

See Generalized pencil-of-function method and Noise (signal processing)

Prony's method

Prony analysis (Prony's method) was developed by Gaspard Riche de Prony in 1795. Generalized pencil-of-function method and Prony's method are signal processing.

See Generalized pencil-of-function method and Prony's method

Radar signal characteristics

A radar system uses a radio-frequency electromagnetic signal reflected from a target to determine information about that target. Generalized pencil-of-function method and radar signal characteristics are radar signal processing.

See Generalized pencil-of-function method and Radar signal characteristics

Residue (complex analysis)

In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.

See Generalized pencil-of-function method and Residue (complex analysis)

Sampling (signal processing)

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. Generalized pencil-of-function method and sampling (signal processing) are signal processing.

See Generalized pencil-of-function method and Sampling (signal processing)

Scattering parameters

Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals.

See Generalized pencil-of-function method and Scattering parameters

Series acceleration

In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series.

See Generalized pencil-of-function method and Series acceleration

Signal processing

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.

See Generalized pencil-of-function method and Signal processing

Signal-to-noise ratio

Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise.

See Generalized pencil-of-function method and Signal-to-noise ratio

Significant figures

Significant figures, also referred to as significant digits or sig figs, are specific digits within a number written in positional notation that carry both reliability and necessity in conveying a particular quantity.

See Generalized pencil-of-function method and Significant figures

Singular value

In mathematics, in particular functional analysis, the singular values of a compact operator T: X \rightarrow Y acting between Hilbert spaces X and Y, are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator T^*T (where T^* denotes the adjoint of T).

See Generalized pencil-of-function method and Singular value

References

[1] https://en.wikipedia.org/wiki/Generalized_pencil-of-function_method

Also known as GPOF, GPOF method, Generalized pencil-of-function, Matrix pencil method, Pencil-of-function method.

Generalized pencil-of-function method, the Glossary

Table of Contents

See also

Computational electromagnetics

Radar signal processing

Signal estimation

References