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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Additive synthesis ： ウィキペディア英語版 Additive synthesis Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together.〔 〕〔 〕 The timbre of musical instruments can be considered in the light of Fourier theory to consist of multiple harmonic or inharmonic ''partials'' or overtones. Each partial is a sine wave of different frequency and amplitude that swells and decays over time. Additive synthesis most directly generates sound by adding the output of multiple sine wave generators. Alternative implementations may use pre-computed wavetables or the inverse Fast Fourier transform. ==Definitions== Harmonic additive synthesis is closely related to the concept of a Fourier series which is a way of expressing a periodic function as the sum of sinusoidal functions with frequencies equal to integer multiples of a common fundamental frequency. These sinusoids are called harmonics, overtones, or generally, partials. In general, a Fourier series contains an infinite number of sinusoidal components, with no upper limit to the frequency of the sinusoidal functions and includes a DC component (one with frequency of 0 Hz). Frequencies outside of the human audible range can be omitted in additive synthesis. As a result, only a finite number of sinusoidal terms with frequencies that lie within the audible range are modeled in additive synthesis. A waveform or function is said to be periodic if : $y(t)\; =\; y(t+P)\; \backslash$ for all $t\; \backslash ,$ and for some period $P\; \backslash ,$. The Fourier series of a periodic function is mathematically expressed as: : $\backslash begin$ y(t) &= \frac + \sum_^ \left(a_k \cos(2 \pi k f_0 t ) - b_k \sin(2 \pi k f_0 t ) \right ) \\ &= \frac + \sum_^ r_k \cos\left(2 \pi k f_0 t + \phi_k \right) \\ \end where :: $f\_0\; =\; 1/P\backslash ,$ is the fundamental frequency of the waveform and is equal to the reciprocal of the period, :: $a\_k\; =\; r\_k\; \backslash cos(\backslash phi\_k)\; =\; 2\; f\_0\; \backslash int\_^P\; y(t)\; \backslash cos(2\; \backslash pi\; k\; f\_0\; t)\backslash ,\; dt,\; \backslash quad\; k\; \backslash ge\; 0\backslash ,$ :: $b\_k\; =\; r\_k\; \backslash sin(\backslash phi\_k)\; =\; -2\; f\_0\; \backslash int\_^P\; y(t)\; \backslash sin(2\; \backslash pi\; k\; f\_0\; t)\backslash ,\; dt,\; \backslash quad\; k\; \backslash ge\; 1\backslash ,$ :: $r\_k\; =\; \backslash sqrt\backslash ,$ is the amplitude of the $k\backslash ,$th harmonic, :: $\backslash phi\_k\; =\; \backslash operatorname(b\_k,\; a\_k)\backslash ,$ is the phase offset of the $k\backslash ,$th harmonic. atan2( ) is the four-quadrant arctangent function, Being inaudible, the DC component, $a\_0/2\backslash ,$, and all components with frequencies higher than some finite limit, $K\; f\_0\backslash ,$, are omitted in the following expressions of additive synthesis. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Additive synthesis」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.