Fourier transformIn physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.
Sine and cosine transformsIn mathematics, the Fourier sine and cosine transforms are forms of the Fourier transform that do not use complex numbers or require negative frequency. They are the forms originally used by Joseph Fourier and are still preferred in some applications, such as signal processing or statistics. The Fourier sine transform of f(t), sometimes denoted by either or , is If t means time, then ξ is frequency in cycles per unit time, but in the abstract, they can be any pair of variables which are dual to each other.
Delay (audio effect)Delay is an audio signal processing technique that records an input signal to a storage medium and then plays it back after a period of time. When the delayed playback is mixed with the live audio, it creates an echo-like effect, whereby the original audio is heard followed by the delayed audio. The delayed signal may be played back multiple times, or fed back into the recording, to create the sound of a repeating, decaying echo. Delay effects range from a subtle echo effect to a pronounced blending of previous sounds with new sounds.
Weierstrass transformIn mathematics, the Weierstrass transform of a function f : R → R, named after Karl Weierstrass, is a "smoothed" version of f(x) obtained by averaging the values of f, weighted with a Gaussian centered at x. Specifically, it is the function F defined by the convolution of f with the Gaussian function The factor 1/√(4π) is chosen so that the Gaussian will have a total integral of 1, with the consequence that constant functions are not changed by the Weierstrass transform. Instead of F(x) one also writes Wf. Non-uniform discrete Fourier transformIn applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.
Quality of serviceQuality of service (QoS) is the description or measurement of the overall performance of a service, such as a telephony or computer network, or a cloud computing service, particularly the performance seen by the users of the network. To quantitatively measure quality of service, several related aspects of the network service are often considered, such as packet loss, bit rate, throughput, transmission delay, availability, jitter, etc.
Asynchronous Transfer ModeAsynchronous Transfer Mode (ATM) is a telecommunications standard defined by the American National Standards Institute and ITU-T (formerly CCITT) for digital transmission of multiple types of traffic. ATM was developed to meet the needs of the Broadband Integrated Services Digital Network as defined in the late 1980s, and designed to integrate telecommunication networks. It can handle both traditional high-throughput data traffic and real-time, low-latency content such as telephony (voice) and video.
Radon transformIn mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line. The transform was introduced in 1917 by Johann Radon, who also provided a formula for the inverse transform. Radon further included formulas for the transform in three dimensions, in which the integral is taken over planes (integrating over lines is known as the X-ray transform).
Queuing delayIn telecommunication and computer engineering, the queuing delay or queueing delay is the time a job waits in a queue until it can be executed. It is a key component of network delay. In a switched network, queuing delay is the time between the completion of signaling by the call originator and the arrival of a ringing signal at the call receiver. Queuing delay may be caused by delays at the originating switch, intermediate switches, or the call receiver servicing switch.
Laplace transformIn mathematics, the 'Laplace transform, named after its discoverer Pierre-Simon Laplace (ləˈplɑ:s), is an integral transform that converts a function of a real variable (usually , in the time domain) to a function of a complex variable (in the complex frequency domain, also known as s-domain', or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms ordinary differential equations into algebraic equations and convolution into multiplication.
