 |
STFT Colored Spectrogram 1000ms
The short-time Fourier transform (STFT) is a List of Fourier-related transforms, Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in Software Defined Radio, software defined radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers. Forward STFT Continuous-time STFT Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
List Of Fourier-related Transforms
This is a list of linear transformations of function (mathematics), functions related to Fourier analysis. Such transformations Map (mathematics), map a function to a set of coefficients of basis functions, where the basis functions are trigonometric function, sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds to a single frequency component. Continuous transforms Applied to functions of continuous arguments, Fourier-related transforms include: * Two-sided Laplace transform * Mellin transform, another closely related integral transform * Laplace transform: the Fourier transform may be considered a special case of Two-sided Laplace transform#Relationship to the Fourier transform, the imaginary axis of the bilateral Laplace transform * Fourier transform, with special cases: ** Fourier series *** When the input function/waveform i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
|
Overlap–add Method
In signal processing, the overlap–add method is an efficient way to evaluate the discrete convolution of a very long signal x /math> with a finite impulse response (FIR) filter h /math>: where h = 0 for m outside the region ,M This article uses common abstract notations, such as y(t) = x(t) * h(t), or y(t) = \mathcal\, in which it is understood that the functions should be thought of in their totality, rather than at specific instants t (see Convolution#Notation). The concept is to divide the problem into multiple convolutions of h /math> with short segments of x /math>: :x_k \triangleq\ \begin x + kL & n = 1, 2, \ldots, L\\ 0, & \text, \end where L is an arbitrary segment length. Then: :x = \sum_ x_k - kL\, and y /math> can be written as a sum of short convolutions: :\begin y = \left(\sum_ x_k - kLright) * h &= \sum_ \left(x_k - kL* h right)\\ &= \sum_ y_k - kL \end where the linear convolution y_k \triangleq\ x_k * h , is zero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
STFT Colored Spectrogram 125ms
The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in software defined radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers. Forward STFT Continuous-time STFT Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for only a short period of time. The Fourier transform (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base units is 1/s or s−1, meaning that one hertz is one per second or the Inverse second, reciprocal of one second. It is used only in the case of periodic events. It is named after Heinrich Hertz, Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. For high frequencies, the unit is commonly expressed in metric prefix, multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Window B
A window is an opening in a wall, door, roof, or vehicle that allows the exchange of light and may also allow the passage of sound and sometimes air. Modern windows are usually glazed or covered in some other transparent or translucent material, a sash set in a frame in the opening; the sash and frame are also referred to as a window. Many glazed windows may be opened, to allow ventilation, or closed to exclude inclement weather. Windows may have a latch or similar mechanism to lock the window shut or to hold it open by various amounts. Types include the eyebrow window, fixed windows, hexagonal windows, single-hung, and double-hung sash windows, horizontal sliding sash windows, casement windows, awning windows, hopper windows, tilt, and slide windows (often door-sized), tilt and turn windows, transom windows, sidelight windows, jalousie or louvered windows, clerestory windows, lancet windows, skylights, roof windows, roof lanterns, bay windows, oriel windows ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Morlet Wavelet
In mathematics, the Morlet wavelet (or Gabor wavelet)0). The parameter \sigma in the Morlet wavelet allows trade between time and frequency resolutions. Conventionally, the restriction \sigma>5 is used to avoid problems with the Morlet wavelet at low \sigma (high temporal resolution). For signals containing only slowly varying frequency and amplitude modulations (audio, for example) it is not necessary to use small values of \sigma. In this case, \kappa_ becomes very small (e.g. \sigma>5 \quad \Rightarrow \quad \kappa_5, the frequency of the Morlet wavelet is conventionally taken to be \omega_\simeq\sigma. The wavelet exists as a complex version or a purely real-valued version. Some distinguish between the "real Morlet" vs the "complex Morlet". Others consider the complex version to be the "Gabor wavelet", while the real-valued version is the "Morlet wavelet". Uses Use in medicine In magnetic resonance spectroscopy imaging, the Morlet wavelet transform method offers an i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Gabor Transform
The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the Sine wave, sinusoidal frequency and phase (waves), phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourier transform to derive the time-frequency analysis.E. Sejdić, I. Djurović, J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” ''Digital Signal Processing'', vol. 19, no. 1, pp. 153-183, January 2009. The window function means that the signal near the time being analyzed will have higher weight. The Gabor transform of a signal ''x''(''t'') is defined by this formula: : G_x(\tau,\omega) = \int_^\infty x(t)e^e^\,dt The Gaussian function has infinite range and it is impractical for implementation. Ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Fourier Uncertainty Principle
In mathematics, the Fourier transform (FT) is an integral transform that takes a function (mathematics), function as input then outputs another function that describes the extent to which various Frequency, frequencies are present in the original function. The output of the transform is a complex number, complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the Operation (mathematics), mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical Chord (music), chord into the sound intensity, intensities of its constituent Pitch (music), pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the #Uncertainty principle, uncerta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Gabor Limit
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known. More formally, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such as position, ''x'', and momentum, ''p''. Such paired-variables are known as complementary variables or canonically conjugate variables. First introduced in 1927 by German physicist Werner Heisenberg, the formal inequality relating the standard deviation of position ''σx'' and the standard deviation of momentum ''σp'' was derived by Earle Hesse Kennard later that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Werner Heisenberg
Werner Karl Heisenberg (; ; 5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers of the theory of quantum mechanics and a principal scientist in the German nuclear program during World War II. He published his Umdeutung paper, ''Umdeutung'' paper in 1925, a major reinterpretation of old quantum theory. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, his matrix mechanics, matrix formulation of quantum mechanics was substantially elaborated. He is known for the uncertainty principle, which he published in 1927. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics". Heisenberg also made contributions to the theories of the Fluid dynamics, hydrodynamics of turbulent flows, the atomic nucleus, ferromagnetism, cosmic rays, and subatomic particles. He introduced the concept of a wave function collapse. He was also instrumental in planning the first West Germa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |