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Discrete sine transform (5601 bytes)
1: ...d functions|odd]] [[symmetry]] (since the Fourier transform of a real and odd function is real and imaginary)... 3: A related transform is the [[discrete cosine transform]] (DCT), which is equivalent to a DFT of real and... 11: ...''<sub>0</sub>, ...., ''x''<sub>''n''-1</sub> are transformed into the ''n'' real numbers ''f''<sub>0</sub>, ... 52: ...e factors of ''n''+1/2 in the denominators of the sine arguments. However, these variants seem to be ra... 54: ==== Inverse Transforms ==== Discrete wavelet transform (2548 bytes) 1: ...velet transform]]s for which the [[wavelet]]s are discretely sampled. 3: ...of <math>2^n</math> numbers, the [[Haar wavelet]] transform may be considered to simply pair up input values,... 5: ...an alternative to the conventional [[Fast Fourier Transform]]. 7: ...rence relation]]s to generate progressively finer discrete samplings of an implicit mother wavelet function,... 9: ...sform]]s are also related to the discrete wavelet transform. Discrete Hankel transform (2167 bytes) 1: ... transform is related to the [[continuous Fourier transform]]. 3: ...he [[unit interval]]. Then the finite ν-Hankel transform of ''f''(''t'') is defined to be the set of numbe... 15: ...s the [[matrix (math)|matrix]] of the ν-Hankel transform of size ''M'' - 1. 17: ...the sampling formula given above. Therefore, this transform corresponds to an orthogonal expansion in [[eigen... 26: [[Category:Transforms]] Discrete cosine transform (8636 bytes) 1: ... odd functions|even]] symmetry (since the Fourier transform of a real and even function is real and even), wh... 3: The most common variant of discrete cosine transform is the type-II DCT, which is often called simply ... 5: ...d'' functions, and the [[modified discrete cosine transform]] (MDCT), which is based on a DCT of ''overlappin... 9: ..., approaching the optimal [[Karhunen-Loève transform]] for signals based on certain limits of [[Markov... 13: ...lated transform, the ''modified'' discrete cosine transform, or [[MDCT]], is used in [[Advanced audio coding|... Discrete Fourier transform (14190 bytes) 1: ...it can be computed quickly using a [[fast Fourier transform]] (FFT) algorithm. 3: ...x''<sub>0</sub>, ..., ''x''<sub>''n''-1</sub> are transformed into the sequence of ''n'' complex numbers ''f... 7: ...]] (<math>i^2=-1</math>), and π is [[Pi]]. The transform is sometimes denoted by the symbol <math>\mathcal... 9: The inverse discrete Fourier transform (IDFT) is given by 13: ...qrt{n}</math> for both the DFT and IDFT makes the transforms [[unitary matrix|unitary]], which has some theor... Discrete Hartley transform (9283 bytes) 1: ...the discrete analogue of the continuous [[Hartley transform]], introduced by [[Ralph Hartley|R. V. L. Hartley... 3: ...ithms for the DHT analogous to the [[fast Fourier transform]] (FFT), the DHT was originally proposed by [[Ron... 7: ...''<sub>0</sub>, ...., ''x''<sub>''n''-1</sub> are transformed into the ''n'' real numbers ''h''<sub>0</sub>, ... 15: ...tor in front of the transform and the sign of the sine term are a matter of convention, and differ in so... 19: ...operator]]. The matrix is invertible; the inverse transformation, which allows one to recover the ''x''<sub>'... Discrete-time Fourier transform (1069 bytes) 1: ...m]] of a function <math>f_n</math> of an integer (discrete) "time" variable ''n'' with an unbounded domain. 3: ...ath> is periodic however, as a consequence of the discreteness of the input. 5: ... unbounded spectrum. The applications of the two transforms, however, are quite different. 13: and its inverse transform recovers <math>f_n</math> by 17: [[Category:Transforms]] Inverse discrete cosine transform (783 bytes) 1: ...osine transform|Discrete Cosine Transform]]''', a transformation step commonly used in software that works wi... Modified discrete cosine transform (11326 bytes) 1: ...ransform]] based on the type-IV [[discrete cosine transform]] (DCT-IV), with the additional property of being... 6: ...transform, the MDST, based on the [[discrete sine transform]], as well as other, rarely used, forms of the MD... 12: ...''<sub>0</sub>, ..., ''x''<sub>2''n''-1</sub> are transformed into the ''n'' real numbers ''f''<sub>0</sub>, ... 16: (The normalization coefficient in front of this transform, here unity, is an arbitrary convention and diffe... 18: ==== Inverse Transform ==== Irrational base discrete weighted transform (816 bytes) 1: ...orm''' (IBDWT) is a variant of the [[fast Fourier transform]] using an [[irrational number|irrational]] base;... 7: ... Crandall]], [[Barry Fagin]]: ''Discrete weighted transforms and large-integer arithmetic'', Mathematics of C... Sine wave (1608 bytes) 1: ...unction|graph]] is identical to the generalized [[sine]] function ''y'' = ''A''sin[''ω''(''x'' &mi... 5: [[Image:Sine_Cosine_Graph.png|right]] 7: ...the same shape but is shifted slightly behind the sine wave on the horizontal axis: <math>\cos{(x -\frac... 9: ...frequencies]] blended together. The technique of transforming a complex waveform into its sinusoidal compone... 11: ...clear" to us; some sounds that approximate a pure sine wave are the "beep" of a computer [[speaker]], or... Sine qua non (646 bytes) 1: '''''Sine qua non''''' or '''''conditio sine qua non''''' is a [[Latin language|Latin]] [[law|... 6: ...r. Therefore, Mr. Wilson's act was the ''conditio sine qua non'' of Margaret's injury. Sine squared (278 bytes) 1: '''Sine squared''' (sin<sup>2</sup> x) is an old notation... Latino sine flexione (1525 bytes) 1: ...ng]] [[Interlingua]], which later replaced Latino sine flexione. 4: ...in without Inflexions] - Information about Latino sine flexione and some writings of Giuseppe Peano 5: ...iginal writing's on this language, blog in latino sine flexione, etc. 9: [[de:Latino sine flexione]] 11: [[fr:Latino sine flexione]] (Surfing on Sine Waves) (2889 bytes) 1: '''''(Surfing on Sine Waves)''''' is an [[electronic music]] and early ... 33: [[Category:Electronica albums|Surfing on Sine Waves]] Abbe sine condition (395 bytes) Adjournment sine die (832 bytes) 1: ...ir seats back. A corporate board might adjourn ''sine die'' if the corporation were being [[sale|sold]]... Sine-Gordon equation (1495 bytes) 1: The '''Sine-Gordon equation''' is a [[partial differential eq... 13: Another equation is also called the '''Sine-Gordon equation''': 25: See also [[Bäcklund transform]]. Topologist's sine curve (2248 bytes) 1: ...tics]] known as [[topology]], the '''topologist's sine curve''' is an example that has several interesti... 9: Two variations of the topologist's sine curve have other interesting properties. 11: ...], but has similar properties to the topologist's sine curve -- it too is [[connected]] but not [[locall... 13: ...urve''' can be defined by taking the topologist's sine curve and adding to it the set {(''x'',1) | ''x''... 16: [[Image:Tsc.png|Topologist's Sine Curve]] Nulla poena sine lege (2014 bytes) 1: ... principle called "''[[Nullum crimen, nulla poena sine praevia lege poenali]]''", which means penal law ... 5: ...to other crimes, so that to satisfy ''Nulla poena sine lege''. 7: ...e that this exercise does not violate nulla poena sine lege, since these acts, even if not prohibited un... 9: ...nd theorists]] would further add that nulla poena sine lege is not violated if the punished act is again... 12: * [[Nullum crimen, nulla poena sine praevia lege poenali]]
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