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Review questions for Chapter 5 (Filter Structure)
The following question is aimed to help you test your understanding of the slide and an d lecture. There are mostly simple conceptual question. Most of the answer can be obtained from the slide and lecture. Slide, topic
$: %ntroduction &. 'S( )i!e the design flow of a digital filter design and implementation *int: &( +escribe +escribe the specifi specification cation ' mention mention passband passband and and stopband stopband cut off off frequency, ma" gain in stopband and minimum gain at passband(. $ ( - ( ( %mplem %mplement ent a suit suitabl ablee struct structure ure / ( 0( #hoo #hoose se a +S1 +S1 proce process ssor or 2( 3r 3rite ite the the code code '# or assem assembly bly(( 4( +ownlo +ownload ad progra program m into into the +S1 +S1 proce processo ssor r $ 'TF( 5 transfer transfer function can ha!e only one on e structure 'true6false( -( 3hy use flow diagram represent a filter structure ( 3hat is a filter structure : %ntr ntro
&.3 &.3hat hat det determ ermine ine an an im implem plemen enttatio ation n com compl ple" e"iity of a par partticul icular ar struct ructur ure e $.*ow does the order of the filter affect the comple"ity -. *ow the order of the filter affect the filter performance
/: System Function and 8##+9
. 'TF( The effect of quanti7ation error depend on the filter structure implemented. &. )i!en an impulse response how can the transfer function and frequency response obtained analytically. analytically. $. *ow can an impulse response of a digital filter obtained e"perimentally -. 3hat does an 8##+9 equation describe
. 9"plain how transform can be used to analy7e an 8T% system
0: System Function and 8##+9
&. %dentify the filter coefficients gi!en the transfer function *'7(. q
∑ bk z
−
H ' z (
=
Y ( z ) X ' z (
=
k
k = p =
∑ ak z
−
k
k
=
=
$. 'TF( The transfer function *'7( define the system beha!ior in time domain 'true6false( 2.
&. %dentify the filter coefficient gi!en the 8##+9 equation below. %s it a F%; or %%; filter 3hat is the order y>n? +
& .
y>n − &? −
4
y>n − $? = x>n? + $ x>n − &? + x> n − $?
$. The following matlab function designs an %%; filter using the elliptic method, order<4, the cut off freq is -==*7, sampling frequency < === *7 >b, a? < ellip'4, ./, /=, -==6$===( The coefficient !ector is gi!en as b < =.==0 @=.=$A =.==0
=.=0// @=.&=A0
=.&$4A @=.&=A0
=.=0// @=.=$A
a< &.==== @0.A-/= $&.//0/ @-A.&/&/ /.-44 @-.-00/ &0./4A0 @.002=./40= 3rite the 8##+9 equation. +raw the direct form $ filter structure.
4: BlocC diagram and signal flow graph
&. Dame the - elements in the blocC diagram or signal flow graph. $. +raw the blocC diagram for the 8##+9 equation. Find the transfer function *'7( y>n?< =./">n? – =.$ ">n@&? E =. ">n@-? y>n?< =./">n? – =.$ ">n@&? E=. y>n@&? y>n?< =./">n? – =.$ ">n@&? E=. y>n@&? E y>n@$?
A.
&= BlocC diagram
&. +ifferentiate between recursi!e and non@recursi!e 8##+9 equation. $. 'TF( The signal flow graph implement the 8##+9 equation
&. )i!en the transfer function below, draw the blocC diagram. 3hat is the order H ' z ( =
& + =.2 z
&
−
+
=.-z $ −
+raw the structure. Find the difference equation. $. +eri!e the difference equation gi!en the structure implementation by the blocC diagram below. 3hat is the order +eri!e the transfer function. %s the filter stable
x>n?
3
y>n?
=.2
-1
z
y>n@&? -1
@$ &$
z
y>n@$?
3hat is the difference between canonic and non canonic filter structure 3hich one is preferable, why
&-
3rite the 8##+9 equation for both the $ structures below and show that they are the same.
9qui!alent structure
&- %%; structure &/@$2 +irect form & and $
&. Dame the - different structures to reali7e a %%; filter.
&. Show that both the structure gi!e the same transfer function *'7(
+irect form & , first order
w&>n?
w$>n?
+irect form $ , first order *int: se w>n? and w$>n? to simplify the 8##+9 equation. *'7(< G'7(6H'7( < G'7(63&'7( I 3&'7(6H'7( 3hich one is canonic and which one is non canonic structure *ow many memory elements required in each structure 9"plain the ad!antage of direct form $ compared with direct form &. -0 @ &
8earn to factori7e polynomial http:66www.wtamu.edu6academic6anns6mps6math6mathlab6colJalgebra6colJalgJt ut2Jfactor.htm http:66www.sosmath.com6algebra6factor6fac=$6fac=$.html Dow try to factori7e this 'without looCing at the slide(. +raw all the different possible reali7ation for cascade structure. =. z & + =.-0$ z $ + =.=$ z −
H ( z )
=
−
−
& + =. z & + =.&4 z $ − =.$ z −
−
−
*'7( < & E 7@& E =.2/7@$ E =.-2/7@- E =.&$/7@ %f you do not Cnow how to factori7e the polynomial, you will not be able to draw the cascade structure. -: 1arallel structure
%n order to get the parallel structure you must master the partial fraction e"pansion method http:66www.swarthmore.edu6DatSci6echee!e&6;ef681S561artialFraction61artial Fraction.html http:66www.purplemath.com6modules6partfrac-.htm 3hat is the ad!antage of parallel structure
