1、Chapter 4LTI Discrete-Time Systemsin the Transform-DomainLecture 2Key Points2Ideal FiltersFrequency responses of the four popular types of ideal digital filters with real impulse response coefficients are shown below:LowpassHighpassBandpassBandstop3Linear-Phase Transfer FunctionsIt is nearly impossi

2、ble to design a linear-phase IIR transfer functionIt is always possible to design an FIR transfer function with an exact linear-phase responseNot all the FIR filters have linear phase response, the condition is:or4Four Types of Linear-Phase FIR Transfer FunctionsType 1: N = 8Type 2: N = 7Type 3: N =

3、 8Type 4: N = 7時域上的特點對稱+偶奇（階）反對稱+偶奇（階）5四種線性相位FIR濾波器的零點所共有的結(jié)構(gòu)Zero Locations of Linear-Phase FIR Transfer Functions6四種線性相位FIR濾波器的零點所獨有的結(jié)構(gòu)Zero Locations of Linear-Phase FIR Transfer Functions1Type 2Type 111Type 4Type 31Linear-Phase FIR Transfer Functions with Zeros N-Filter Order, number of zeros, (fil

4、ter length-1) Step 1: find the mirror-image pairs of given zeros;Step 2: write down the particular zeros for the given type of linear-phase FIR filters;Step 3:represent the transfer function in the factored form.8Design Tips of Linear-Phase FIR FilterA Type 2 FIR filter cannot be used to design a hi

5、ghpass filter since it always has a zeroA Type 3 FIR filter has zeros at both z = 1 and , and hence cannot be used to design either a lowpass or a highpass or a bandstop filter9Design Tips of Linear-Phase FIR FilterA Type 4 FIR filter is not appropriate to design a lowpass filter due to the presence of a zero at z = 1A Type 1 FIR fil