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29 relations: Absolute convergence, Aliasing, Anti-aliasing filter, Autocorrelation, Émile Borel, Bandlimiting, Claude Shannon, Convolution, Dirac comb, Discrete time and continuous time, E. T. Whittaker, Fourier transform, Hölder's inequality, Hertz, John Macnaghten Whittaker, Low-pass filter, Lp space, Nyquist frequency, Nyquist–Shannon sampling theorem, Rectangular function, Sampling (signal processing), Signal, Sinc filter, Sinc function, Spatial anti-aliasing, Spectral density, Stationary process, Uniform convergence, Wiener–Khinchin theorem.
Absolute convergence
In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite.
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Aliasing
In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled.
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Anti-aliasing filter
An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to approximately or completely satisfy the sampling theorem over the band of interest.
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Autocorrelation
Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay.
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Émile Borel
Félix Édouard Justin Émile Borel (7 January 1871 – 3 February 1956) was a French mathematician and politician.
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Bandlimiting
Bandlimiting is the limiting of a signal's frequency domain representation or spectral density to zero above a certain finite frequency.
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Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".
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Convolution
In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
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Dirac comb
In mathematics, a Dirac comb (also known as an impulse train and sampling function in electrical engineering) is a periodic tempered distribution constructed from Dirac delta functions for some given period T. The symbol \operatorname(t), where the period is omitted, represents a Dirac comb of unit period.
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Discrete time and continuous time
In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.
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E. T. Whittaker
Edmund Taylor Whittaker FRS FRSE (24 October 1873 – 24 March 1956) was an English mathematician who contributed widely to applied mathematics, mathematical physics, and the theory of special functions.
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Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
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Hölder's inequality
In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of ''Lp'' spaces.
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Hertz
The hertz (symbol: Hz) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second.
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John Macnaghten Whittaker
John Macnaghten Whittaker FRS (7 March 1905 – 29 January 1984) was a British mathematician and Vice-Chancellor of the University of Sheffield from 1953 to 1965.
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Low-pass filter
A low-pass filter (LPF) is a filter that passes signals with a frequency lower than a certain cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency.
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Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
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Nyquist frequency
The Nyquist frequency, named after electronic engineer Harry Nyquist, is half of the sampling rate of a discrete signal processing system.
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Nyquist–Shannon sampling theorem
In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals").
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Rectangular function
The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as: 0 & \mbox |t| > \frac \\ \frac & \mbox |t|.
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Sampling (signal processing)
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.
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Signal
A signal as referred to in communication systems, signal processing, and electrical engineering is a function that "conveys information about the behavior or attributes of some phenomenon".
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Sinc filter
In signal processing, a sinc filter is an idealized filter that removes all frequency components above a given cutoff frequency, without affecting lower frequencies, and has linear phase response.
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Sinc function
In mathematics, physics and engineering, the cardinal sine function or sinc function, denoted by, has two slightly different definitions.
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Spatial anti-aliasing
In digital signal processing, spatial anti-aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high-resolution image at a lower resolution.
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Spectral density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal.
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Stationary process
In mathematics and statistics, a stationary process (a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.
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Uniform convergence
In the mathematical field of analysis, uniform convergence is a type of convergence of functions stronger than pointwise convergence.
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Wiener–Khinchin theorem
In applied mathematics, the Wiener–Khinchin theorem, also known as the Wiener–Khintchine theorem and sometimes as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that the autocorrelation function of a wide-sense-stationary random process has a spectral decomposition given by the power spectrum of that process.
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References
[1] https://en.wikipedia.org/wiki/Whittaker–Shannon_interpolation_formula
