文档介绍：Fourier Series
电子技术系:刘佳
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Content
Fourier Series and Fourier Transform
Analysis and Synthesis
Periodic Phenomenon and Function
Trigonometric function
Fourier plex Form of the Fourier Series
Detail of Fourier Series
Fourier Series
Fourier Series and Fourier Transform
Fourier
Fourier Series
Almost periodic phenomenon
Fourier Transform
Non-periodic phenomenon
一些概念上是通用的,一些则不通用
Fourier Series
Analysis and Synthesis
Fourier analysis
The process of posing a musical instrument sound or any other periodic function into its constituent sine or cosine waves is called Fourier analysis
F ( x ) = a /2 + a 1 cos x + b 1 sin x + a 2 cos 2 x + b 2 sin 2 x + ... + a n cos nx + b n sin nx + ...
Fourier synthesis
Fourier synthesis works bining a sine wave signal and sine-wave or cosine-wave harmonics (signals at multiples of the lowest, or fundamental, frequency) in certain proportions.
F ( x ) = a /2 + a 1 cos x + b 1 sin x + a 2 cos 2 x + b 2 sin 2 x + ... + a n cos nx + b n sin nx + ...
Linear Operation
Fourier synthesis and analysis based on Linear Operation: Integration and series.
Fourier Transform is part of linear systems.
Fourier Series
Periodic Phenomenon & Functions
Periodic Phenomenon
Generally speaking we think about periodic phenomena according to whether they are periodic in time or periodic in space.