Feb.2008DISP Lab1 FIR and IIR Filter Design Techniques FIR 與 IIR 濾波器設計技巧 oSpeaker: Wen-Fu Wang 王文阜 oAdvisor: Jian-Jiun Ding 丁建均 教授 oE-mail: r96942061ntu.edu.tw oGraduate Institute of Communication Engineering oNational Taiwan University, Taipei, Taiwan, ROC Feb.2008DISP Lab2 Outline o Introduction o IIR Filter Design by Impulse invariance method o IIR Filter Design by Bilinear transformation method o FIR Filter Design by Window function technique Feb.2008DISP Lab3 Outline o FIR Filter Design by Frequency sampling technique o FIR Filter Design by MSE o Conclusions o References Feb.2008DISP Lab4 Introduction o Basic filter classification o We put emphasis on the digital filter now, and will introduce to the design method of the FIR filter and IIR filter respectively. Filter Analog Filter Digital Filter IIR Filter FIR Filter Feb.2008DISP Lab5 Introduction o IIR is the infinite impulse response abbreviation. o Digital filters by the accumulator, the multiplier, and it constitutes IIR filter the way, generally may divide into three kinds, respectively is Direct form, Cascade form, and Parallel form. Feb.2008DISP Lab6 Introduction o IIR filter design methods include the impulse invariance, bilinear transformation, and step invariance. o We must emphasize at impulse invariance and bilinear transformation. Feb.2008DISP Lab7 Introduction o IIR filter design methods Continuous frequency band transformation Impulse Invariance method Bilinear transformation method Step invariance method IIR filter Normalized analog lowpass filter Feb.2008DISP Lab8 Introduction o The structures of IIR filter Direct form 1 Direct form2 b0 b1 b2 b2 b1 b0 -a1 -a2 -a1 -a2 x(n)x(n)Y(n)Y(n) Feb.2008DISP Lab9 Introduction o The structures of IIR filter Cascade form x(n)Y(n) b0 b1 b2 -a1 -a2 -c1 -c2 d1 d2 Parallel form Y(n)x(n) b1 b0 d1 d0 E -c1 -c2 -a1 -a2 Feb.2008DISP Lab10 Introduction o FIR is the finite impulse response abbreviation, because its design construction has not returned to the part which gives. o Its construction generally uses Direct form and Cascade form. Feb.2008DISP Lab11 Introduction o FIR filter design methods include the window function, frequency sampling, minimize the maximal error, and MSE. o We must emphasize at window function, frequency sampling, and MSE. Window function technique Frequency sampling technique Minimize the maximal error FIR filter Mean square error Feb.2008DISP Lab12 Introduction o The structures of FIR filter x(n)x(n) b1 b2 b3 b4 b0 Y(n)Y(n) Direct formCascade form b1 b2 d1 d2 b0 Feb.2008DISP Lab13 IIR Filter Design by Impulse invariance method o The most straightforward of these is the impulse invariance transformation o Let be the impulse response corresponding to , and define the continuous to discrete time transformation by setting o We sample the continuous time impulse response to produce the discrete time filter Feb.2008DISP Lab14 IIR Filter Design by Impulse invariance method o The frequency response is the Fourier transform of the continuous time function and hence Feb.2008DISP Lab15 IIR Filter Design by Impulse invariance method o The system function is o It is the many-to-one transformation from the s plane to the z plane. Feb.2008DISP Lab16 IIR Filter Design by Impulse invariance method o The impulse invariance transformation does map the -axis and the left-half s plane into the unit circle and its interior, respectively Re(Z) Im(Z) 1 S domainZ domain Feb.2008DISP Lab17 IIR Filter Design by Impulse invariance method o is an aliased version of o The stop-band characteristics are maintained adequately in the discrete time frequency response only if the aliased tails of are sufficiently small. 0 Feb.2008DISP Lab18 IIR Filter Design by Impulse invariance method o The Butterworth and Chebyshev-I lowpass designs are more appropriate for impulse invariant transformation than are the Chebyshev-II and elliptic designs. o This transformation cannot be applied directly to highpass and bandstop designs. Feb.2008DISP Lab19 IIR Filter Design by Impulse invariance method o is expanded a partial fraction expansion to produce o We have assumed that there are no multiple poles o And thus Feb.2008DISP Lab20 IIR Filter Design by Impulse invariance method o Example: Expanding in a partial fraction expansion, it produce The impulse invariant transformation yields a discrete time design with the system function Feb.2008DISP Lab21 IIR Filter Design by Bilinear transformation method o The most generally useful is the bilinear transformation. o To avoid aliasing of the frequency response as encountered with the impulse invariance transformation. o We need a one-to-one mapping from the s plane to the z plane. o The problem with the transformation is many-to-one. Feb.2008DISP Lab22 IIR Filter Design by Bilinear transformation method o We could first use a one-to-one transformation from to , whic