第02章 离散时&eacu

第02章 离散时&eacu

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2.3 frequency-domain representation of discrete-time signal and system 2.3.1 definition of Fourier transform 2.3.2 frequency response of system 2.3.3 properties of Fourier transform
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Hz f Hz f t t t x 200 , 100 ), 200 2 cos( 5 . 0 ) 100 2 cos( ) ( 2 1 = = + = π 0 0.01 0.02 -1 0 1 2 0 100 200 300 400 500 0 5 10 EXAMPLE 信号的频域表示 的直观意义 时域表示 频域表示
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对于声音信号:信号的频谱决定了 音调 (基音的频率)、 音强 (幅度)和 音色 (泛音)。 对于图像信号:低频代表基本形状和亮度; 高频代表细节。 EXAMPLE 低通滤波后 高通滤波后
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EXAMPLE 频域分析应用于对图像信号的带阻去噪
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2.3.1 definition of Fourier transform (离散时间傅立叶变换) Many sequences can be represented by a Fourier integral of the form ω π d e e X n x n j j = ) ( 2 1 ] [ inverse Fourier transform () +∞ −∞ = = n n j j e n x e X ] [ where Fourier transform 0 | ] [ = +∞ −∞ = = j n e X n x 0 | ] [ 2 ) ( = = n j n x d e X 证明正变换的结果能通过反变换合成原始信号见课堂笔记
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) () |() | j jj j X e RI Xe X e jX e e ω ωω =+ = ( ( ) magnitude e X j |, | , j X e phase ( ( ) [ ] phase value principal e X ARG j : π < < ( ) [ ] phase continuous e X j , arg In general, the Fourier transform is a complex-valued function of . ( ) j n j j e X e n x e X +∞ + + = = ) 2 ( ) 2 ( ] [ Periodicity
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subplot(2,2,1); fplot ('real(1/(1-0.2*exp(-1*j*w)))',[-2*pi,2*pi]); title(' 实部 ') subplot(2,2,2); fplot('imag(1/(1-0.2*exp(-1*j*w)))',[-2*pi ,2*pi]); title(' 虚部 ') subplot(2,2,3); fplot('abs(1/(1-0.2*exp(-1*j*w)))',[-2*pi,2*pi]); title(' 幅度 ') subplot(2,2,4); fplot('angle(1/(1-0.2*exp(-1*j*w)))',[-2*pi,2*pi]); title(' 相位 ') ω j j n e e X n u n x = = 2 . 0 1 1 ) ( ], [ 2 . 0 ] [ -5 0 5 0.5 1 1.5 实部 -5 0 5 -0.5 0 虚部 -5 0 5 1 幅度 -5 0 5 0 相位 EXAMPLE 从时域理解为什 么有周期性? MATLAB 画信号频谱
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< < −∞ = n n n n x c , ) sin( ] [ π ω > = c c j e X | | , 0 | | , 1 ) ( EXAMPLE ( ) n n d e e X IFT c n j j c c ) sin( 2 1 ] [ = = Sufficient condition for existence of Fourier transform absolutely summable (绝对可和) .
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This note was uploaded on 02/29/2012 for the course EE 325 taught by Professor Lilili during the Fall '11 term at BYU.

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第02章 离散时&eacu

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