Fourier Series Jean Baptiste Joseph Fourier French17631830 Fourier

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Fourier Series

Fourier Series

Jean Baptiste Joseph Fourier (French)(1763~1830)

Jean Baptiste Joseph Fourier (French)(1763~1830)

Fourier Series l 任一週期(periodic)函數可以分解成許多不同振幅 (amplitude),不同頻率(frequency)的 ¡ 正弦(sinusoidal)諧波(harmonic) 與 ¡ 餘弦(cosinusoidal)諧波(harmonic) 的合成(composition)

Fourier Series l 任一週期(periodic)函數可以分解成許多不同振幅 (amplitude),不同頻率(frequency)的 ¡ 正弦(sinusoidal)諧波(harmonic) 與 ¡ 餘弦(cosinusoidal)諧波(harmonic) 的合成(composition)

三種諧波(harmonic )

三種諧波(harmonic )

Adding harmonics

Adding harmonics

快速傅利葉轉換原理 l. A complex nth root of unity is a complex number z such

快速傅利葉轉換原理 l. A complex nth root of unity is a complex number z such that zn = 1. ¡ n = e 2 i / n = principal n th 3 root of unity. 4 = -1 i t ¡e = cos t + i sin t. ¡i 2 = -1. 5 ¡There are exactly n roots of unity: nk, k = 0, 1, . . . , n-1. 2 = i 1 0 = 1 7 6 = -i