1、,6 Time and frequency characterization of S&S,本章要求: 了解LTI系統(tǒng)頻率響應(yīng)的幅度相位表示. 了解理想頻率選擇濾波器的時(shí)域特性,6 Time and frequency characterization of S&S,6.1 The Magnitude-phase Representation of the Fourier Transform,For signal x(t) :,6 Time and frequency characterization of S&S,provides us with the information about

2、the relative magnitudes of the complex exponentials that make up x(t).,provides us with the information concerning the relative phases of these complex exponentials .,have a significant effect on the nature of the signal x(t).,6 Time and frequency characterization of S&S,6 Time and frequency charact

3、erization of S&S,6 Time and frequency characterization of S&S,的變化會(huì)導(dǎo)致信號(hào)x(t)的時(shí)域特性的改變。,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,6.2 The Magnitude-phase Representation of the Frequency Response of LTI System,System characterization:,Impulse response:,Freq

4、uency response:,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,所以，輸入信號(hào)通過(guò)一個(gè)系統(tǒng)后，是否會(huì)有失真，主 要由系統(tǒng)頻率響應(yīng)的相位決定。,6.2.1 Linear and Nonlinear Phase,Linear phase:,Nonlinear phase:,Example:,Effect: Linear phase means non-distortion of signal transmission.,6 Time and frequ

5、ency characterization of S&S,6 Time and frequency characterization of S&S,all-pass system: the gain |H(j| of a system is a nonzero constant for all frequency 。,所以，全通系統(tǒng)的特性完全由它的相位決定。,Definition:,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,不失真?zhèn)鬏數(shù)臈l件： 信號(hào)通過(guò)一個(gè)系

6、統(tǒng)進(jìn)行不失真?zhèn)鬏敚湎到y(tǒng)頻率響應(yīng)必須滿足兩個(gè)條件： 1）頻率響應(yīng)的模必須為常數(shù) 2）頻率響應(yīng)的相位是過(guò)零點(diǎn)的角頻率的線性函數(shù)。即,6.2.3 Log-Magnitude and Bod Plots（波特圖）,Magnitude spectrum:,Phase spectrum:,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,使用波特圖的好處： 將相乘運(yùn)算變?yōu)橄嗉舆\(yùn)算。,6 Time and frequency characterization of S&S,6.

7、3 Time-Domain Properties of Ideal Frequency- selective Filters,1. Ideal lowpass filter with zero phrase:,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,6 Time and freq

8、uency characterization of S&S,Discrete-time ideal lowpass filter with zero phrase:,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,2. Ideal lowpass filter with linear phrase,6 Time and frequency characterization of S&S,6 Time and frequency characterization of S&S,Example:,Lowpass filte