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1、1,Chapter7 LTI Discrete-Time Systems in the Transform Domain,Transfer Function ClassificationTypes of Linear-Phase Transfer FunctionsSimple Digital Filters,2,Types of Transfer Functions,The time-domain classification of a digital transfer function based on the length of its impulse response sequence
2、:- Finite impulse response (FIR) transfer function.- Infinite impulse response (IIR) transfer function.,3,Types of Transfer Functions,In the case of digital transfer functions with frequency-selective frequency responses, there are two types of classifications:(1) Classification based on the shape o
3、f the magnitude function |H(ei)|. (2) Classification based on the form of the phase function ().,4,7.1 Transfer Function Classification Based on Magnitude Characteristics,Digital Filters with Ideal Magnitude ResponsesBounded Real Transfer FunctionAllpass Transfer Function,5,7.1.1 Digital Filters wit
4、h Ideal Magnitude Responses,A digital filter designed to pass signal components of certain frequencies without distortion should have a frequency response equal to 1 at these frequencies, and should have a frequency response equal to 0 at all other frequencies.,6,Digital Filters with Ideal Magnitude
5、 Responses,The range of frequencies where the frequency response takes the value of 1 is called the passband.The range of frequencies where the frequency response takes the value of 0 is called the stopband.,7,Digital Filters with Ideal Magnitude Responses,Magnitude responses of the four popular typ
6、es of ideal digital filters with real impulse response coefficients are shown below:,8,Digital Filters with Ideal Magnitude Responses,The frequencies c, c1, and c2 are called the cutoff frequencies.An ideal filter has a magnitude response equal to 1 in the passband and 0 in the stopband, and has a 0
7、 phase everywhere.,9,Digital Filters with Ideal Magnitude Responses,Earlier in the course we derived the inverse DTFT of the frequency response HLP(ej)of the ideal lowpass filter: hLPn=sincn/n, - n0, ( |H(ej)|2 )max = K2/(1- )2 | =0 ( |H(ej)|2 ) min = K2/(1+ )2 | =On the other hand, for 0, (2cos )ma
8、x = -2 | = (2cos )min = 2 | =0Here, ( |H(ej)|2 )max = K2/(1+ )2 | = ( |H(ej)|2 )min = K2/(1- )2 | = 0,19,Bounded Real Transfer Functions,Hence,is a BR function for K(1-),Plots of the magnitude function for =0.5 with values of K chosen to make H(z) a BR function are shown on the next page.,20,Bounded Real Transfer Functions,
