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From Fig. a

X1(Z)= X(ZL)Y1(Z)=a1

X(ZL)Y1(Z)=a2

X(ZL)

From Fig. b

Y1(Z)=a1

X(ZL)Y1(Z)=a2

X(ZL)

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Fifth Identity

x(n) L =

x(n)

Fig.a

Fig.b

Z-1y(n) L Z

-L y(n)

x1(n)

x2(n)

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From Fig. a

X1(Z)= Z-1X(Z)

Y(Z)= X1(ZL) = Z-

LX(ZL)

From Fig. b

X2(Z)= X(ZL)

Y(Z)= Z-LX(ZL)

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Sixth Identity

X(Z) L =

X(Z)

Fig.a

Fig.b

G(

Z)

Y(Z) L

G(ZL)

Y(Z)

X1(Z)

X2(Z)

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From Fig.

aX1(Z)=

G(Z)X(Z)Y(Z)= X1(ZL)

=

X(ZL)G(ZL)

From Fig. b

X2(Z)= X(ZL)Y(Z)=

X(ZL)G(ZL)

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Cascadin Sa!"#e $ateCon%erters

x(n)

Hd(

Z)LHu(

Z)

M

y(n)

Intero!ator

"e#imator

FLF

LF$M

x(n)

H(Z)L M

y(n)

FLF

LF$M

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&u#tistae i!"#e!entation of

sa!"#in rate con%erters

x(n)

%1(n)

L1

y(n)

Fx

I& L'' 1 t%en

L1

Fx

%1(n)

L2

L1L2

Fx

%n(n)

Ln

Fy=

LFx

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&u#tistae i!"#e!entation of

sa!"#in rate con%erters

x(n)

M1

%1(n)

y(n)

FxFx$M

1

%2(n)

Fx$M1

M2

Mn

%n(n)

Fy=

Fx$M

I& M'' 1 t%en

M2

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!i#ation*

In hih 'ua#ity data ac'uisition storaesyste!s

In audio sina# "rocessin

In %ideo *+L ,SC run at di.erentsa!"#in rates/ herefore to 0atch an+!erican "rora! in uro"e one needs asa!"#in rate con%erter/

In s"eech "rocessin to reduce the storaes"ace or the trans!ittin rate of s"eechdata/

In trans!u#ti"#exers