Lesson_21

# Lesson_21 - Lesson21 Challenge20 Lesson21:IIRFilters...

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Lesson 21 Challenge 20 Lesson 21:  IIR Filters Challenge 21

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Challenge 20 Design a heuristic 7th order lowpass FIR having a passband frequencies of  ω   = { -2 π /7, 0, 2 π /7}. Q:  What is H(z)? Is the filter linear or non-linear phase? If linear phase , what is the FIRs group delay? --------------------------------------------------------------------- The design of the heuristic FIR requires that the pole-zero cancellation  occurs at the passband frequencies of  ω  = { -2 π /7, 0, 2 π /7} and filter zeros  exist at  ω  = { -6 π /7, -4 π /7, 4 π /7, 6 π /7}.
Challenge 20 » h2=[1,-(cos(4*pi/7)+i*sin(4*pi/7))];  { ω  =4 π /7} » h3=[1,-(cos(6*pi/7)+i*sin(6*pi/7))];  { ω  =6 π /7} » h4=[1,-(cos(8*pi/7)+i*sin(8*pi/7))];  { ω  =-6 π /7 = 8 π /7 } » h5=[1,-(cos(10*pi/7)+i*sin(10*pi/7))];  { ω  =-4 π /7 = 10 π /7 } » h=conv(conv(conv(h2,h3),h4),h5); » y=conv(h,zeros(1,100)); » plot(abs(fft(y))) » y=conv(h,[1,zeros(1,100)]); » plot(abs(fft(y))) » zplane(h,1) h =    1.0000   2.2470   2.8019   2.2470  1.0000    {linear phase} Therefore H(z) = 1 + 2.24 z -1  + 2.80z -2  +2.24 z -3  + z -4

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Challenge 20
Challenge 20 >> [h,w]=freqz(h,1); >> h=[1, 2.24, 2.8, 2.24, 1]; >> [h,w]=freqz(h,1); >> plot(180*angle(h)/pi); >> plot(w,180*angle(h)/pi); π /2 π Slope m=-2

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Lesson 21 Infinite Impulse Response (IIR) Filters or Recursive Filters
Lesson 21 IIRs If a 0 =1, the system is called  monic .   The coefficient a i  define the feedforward path and b i  the feedback path.  In  most cases, M N, where M normally defines the order of the filter.  If initial conditions are zero, system is said to be  at-rest . - + - = = = M 0 m m N 1 m m 0 m] x[k b m] y[k a a 1 y[k]

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Lesson 21 Impluse response Complicated
Lesson 21 Example y[n]=0.8 y[n-1]+5x[n] n= h[n] s[n] 0 h[0]=(0.8*0+5)=5 s[0]=(0.8*0+5)=5 1 h[1]=(0.8*5+0) = 0.8*5

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## This note was uploaded on 08/21/2010 for the course EEL 3135 taught by Professor ? during the Spring '08 term at University of Florida.

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Lesson_21 - Lesson21 Challenge20 Lesson21:IIRFilters...

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